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References
Part I
Modem Treatments of Differential Geometry for Physicists
W. Thirring: A Course in Mathematical PhYSics, Vol. 1, (Springer 1978); Vol. 2 (Springer 1979)
2 Y. Choquet-Bruhat, C. De Witt-Morette, M. Dillard-Bleick: Analysis, Manifolds and Physics, rev. ed. (North-Holland 1982)
3 G. von Westenholz: Differential Forms in Mathematical Physics (North-Holland 1978)
4 R Abraham, J.E. Marsden: Foundations of Mechanics, 2nd ed. (Benjamin 1978)
Short Selection of Mathematical Books
5 S. Kobayashi, K Nomizu: Foundations of Differential Geometry, I, II (Interscience Publishers 1963/69)
6 Y. Matsushima: Differentiable Manifolds (Marcel Dekker, New York 1972) 7 R Sulanke, P. Wintgen: Differentialgeometrie und FaserbUndel (Birkhiiuser 1972) 8 RL. Bishop, RJ. Goldberg: Tensor Analysis on Manifolds (McMillan, New York
1968)
Partll
Oassical Textbooks
9 W. Pauli: Theory of Relativity (Pergamon Press 1958) 10 H. Weyl: Space-Time-Matter; transl. by H.L. Brose, Nethuen, London 1922 (Springer
1970) 11 AS. Eddington: The Mathematical Theory of Relativity (Chelsea Publishing Com
pany 1975)
Recent Books
12 L.D. Landau, E.M. Lifschitz: The Classical Theory of Fields, 4th rev. ed. (Addison-Wesley 1969)
13 S. Weinberg: Gravitation and Cosmology (Wiley & Sons 1972) 14 C.W. Misner, KS. Thome, J.A. Wheeler: Gravitation (Freeman 1973) 15 G. Ellis, S. Hawking: The Large Scale Structure of Space-Time (Cambridge
University Press 1973) 16 RU. Sexl, H.K. Urbantke: Gravitation und Kosmologie. 2. Aufl. (Bibliographisches
lnstitut, Mannheim 1983)
442 References
17 RAdler, M. Bazin, M. Schiffer: Introduction to General Relativity, 2nd ed. (McGraw-Hill 1975)
18 IL. Synge; Relativity, The General Theory (North-Holland 1971) 19 W. Thirring: A Course in Mathematical Physics, Vol. 2, (Springer 1979) 20 J. Ehlers: Survey of General Relativity Theory. In Relativity, Astrophysics and
Cosmology, ed. by W. Israel (Reidel 1973)
Einstein Centenary Collections
21 General Relativity, An Einstein centenary survey, ed. by S.W. Hawking, W. Israel (Cambridge University Press 1979)
22 Einstein Commemorative Volume, ed. by A. Held (Plenum 1980)
Parts nand nI: Quoted References
23 S. Deser: General Relativity and Gravitation, 1,9 (1970) 24 D. Lovelock: 1. Math. Phys. 13,874 (1972) 25 L. Rosenfeld: Mem. Roy. Acad. Belg. CI. Sci. 18, No.6 (1940) 26 E.B. Forrnalont, R.A. Sramek: Astrophys. J. 199, 749 (1975); Phys. Rev. Lett. 36,
1475 (1976); Comm. Astrophys. 7, 19 (1977) 27 RD. Reasenberg et al.: Astrophys. J. 234, L 219 (1979) 28 1.B. Hartle: Phys. Reports 46,201 (1978) 29 1.M. Weisberg, 1.H. Taylor: Gen. ReI. + Grav. 13, I (1981); Astrophys. 1. 253,908
(1982) 30 T.A. Weaver et al.: Astrophys. J. 225, 1021 (1978) 31 S. Chandrasekhar: Am. Jour. Phys. 37, 577 (1969); KC. Wali: Physics Today,
October 1982, p.33 32 KS. Thome: In High Energy Astrophysics, Lectures given at the Summer School at
Les Houches (Gordon & Breach, New York) p.259 33 V. Canuto: Ann. Rev. Astron. Ap. 12, 167 (1974); Ann. Rev. Astron. Ap. 13, 335
(1975) 34 G. Baym, e. Pethick: Ann. Rev. Nucl. Sci. 25,27 (1975); Ann. Rev. Astron. Ap. 17,
415 (1979) 35 W.D. Arnett, R.L. Bowers: Ap. J. Supp!. 33,415 (\977) 36 B. Friedman, Y.R Pandharipande: Nuc!. Phys. A 361, 502 (1981) 37 G. Baym et al.: Nucl. Phys. A 175,225 (1971); Astrophy. J. 170,99 (1972) 38 N. Straumann: Weak Interactions and Astrophysics, Proceedings of the GIFT
Seminar on Electro-Weak Interactions, Peniscola (Spain), May 1980, to be published 39 DJ. Helfand et al.: Nature 283,337 (1980) 40 H Y. Chiu: Stellar Physics (Blaisdell 1968) Chap. 4 41 G. Glen, P. Sutherland: Astrophys. 1. 239,671 (1980) 42 T. Takabuka: Progr. Theor. Phys. 48, 1517 (1972) 43 G. Flowers: Astrophys. J. 180,911 (1973); 190,381 (1974) 44 e.G. Testa, M.A. Ruderman: Phys. Rev. 180, 1227 (1969) 45 J.w. Negele, D. Vautherin: Nucl. Phys. A 207, 298 (1973) 46 B.L. Friman, O.v. Maxwell: Astrophys. J. 232,541 (1979) 47 G. Baym et al.: In Mesons and Fields in Nuclei, ed. by M. Rho, D. Wilkinson
(North-Holland 1978) 48 S.O. Biickmann, W. Weise: In Mesons and Fields in Nuclei, ed. by M. Rho,
D. Wilkinson (North-Holland 1978) 49 O. Maxwell et al.: Astrophys. 1. 216, 77 (1977) 50 M.A. Ruderman et al.: Astrophys. 1. 205,541 (1976) 51 Ch. Kindl, N. Straumann: Helv. Phys. Acta 54,214 (1981) 52 RP. Kerr: Phys. Rev. Lett. 11,237 (1963) 53 E.T. Newman, A. I. Janis: J. Math. Phys. 6,915 (1965)
54 E.T. Newman et al.: J. Math. Phys. 6,918 (1965) 55 G.e. Debney et al.: J. Math. Phys. 10, 1842 (1969)
References 443
56 R Giacconi: The Einstein X-Ray Observatory, Scientific American, February 1980 57 J. TrUmper et al.: Astrophys. J. (Lett) 219, L 105 (1978) 58 G. Boerner: Phys. Rep. 60, 151 (1980) 59 J.N. Bahcall: Ann. Rev. Astron. Ap. 16,241 (1979) 60 W.H.G. Lewin, P.e. Joss: Space Science Rev. 28,3 (1981) 61 E. Flowers, N. Itoh: Astrophys. J. 206,218 (1976) 62 J. van Paradijs: Nature 274, 650 (1978) 63 E.P.J. Van den Heuve1: Enrico Fermi Summer School on Physics and Astrophysics of
Neutron Stars and Black Holes, Course 65 (North-Holland 1978) 64 A Ashtekar, RO. Hansen: J. Math. Phys. 19,549 (1978) 65 R Schoen, S.T. Yau: Commun. Math. Phys. 65,45 (1976); Phys. Rev. Lett. 43, 1457
(1979); Commun. Math. Phys. 79,231 (1981); Commun. Math. Phys. 79,47 (1981) 66 T. Parker, Ch. Tauber: Commun. Math. Phys. 84,223 (1982) 67 e.M Will: Theory and Experiment in Gravitational Physics (Cambridge University
Press 1981) 68 e.V. Vishveshwara: Phys. Rev. D 1,2870 (1970) 69 FJ. Zerilli: Phys. Rev. Lett. 24,737 (1970) 70 RA Hulse, J.H. Taylor: Astrophys. J. 195, LSI (1975) 7I J.H. Taylor, J.M Weisberg: Astrophys. J. 253,908 (1982) 72 R Epstein: Astrophys. J. 216,92 (1977); Astrophys. J. 231,644 (1979); R. Blandford,
SA Teukolsky: Astrophys. J. 2OS, 580 (1976) 73 M Schwarzschild: Structure and Evolution of the Stars (Princeton University Press
1958) 74 L.L. Smarr, R.: Blandford: Astrophys. J. 207,574 (1976) 75 D.H. Roberts, AR. Masters, W.D. Arnett: Astrophys. J. 203, 196 (1976) 76 P. Crane, J.E. Nelson, J.A Tyson: Nature 280, 367 (1979); K.H. Elliott et al.: Mon.
Not. Roy. Astr. Soc. 192,51 (1980) 77 S. Chandrasekhar: An Introduction to the Study of Stellar Structure (University of
Chicago Press 1939) 78 F.1. Dyson, A Lenard: J. Math. Phys. 8,423 (1967); 1. Math. Phys. 9,698 (1968) 79 E.H. Lieb, W.E. Thirring: Phys. Rev. Lett 35,687 (1975), see ibid. 1116 for errata 80 FJ. Dyson: J. Math. Phys. 8, 1538 (1967) 81 P. Ehrenfest: Collected Scientific Papers, ed. by MJ. Klein (North-Holland,
Amsterdam 1959) p. 617 82 E.H. Lieb: Rev. Mod. Phys. 48,553 (1976) 83 W.E. Thirring: A Course in Mathematical Physics, Vol. 4 (Springer 1982) 84 W.E. Thirring: In Rigorous Atomic and Molecular Physics, ed. by G. Velo, AS.
Wightman (plenum Press 1981) 85 J.-M Levy-Leblond: J. Math. Phys. 10,806 (1969) 86 E.E. Salpeter: Astrophys. J. 134,669 (1961) 87 T. Hamada, E.E. Salpeter: Astrophys. J. 134,683 (1961) 88 L.D. Landau: Phys. Z. Sowjetunion 1,285 (1932) 89 V. Trimp1e: Rev. Mod. Phys. 54, 1183 (1982); Rev. Mod. Phys. 55,511 (1983) 90 J.e. Wheeler: Rep. Progr. Phys. 44, 85 (1981) 91 MJ. Rees, RJ. Stoneham (eds.): Supernovae (Reidel, Dordrecht 1982) 92 K. Nomoto: Astrophys. J. 253,798 (1982) 93 S.E. Woosley, T.A Weaver: In Nuclear Astrophysics, ed. by e. Barnes, D. Clayton,
and D. Schramm (Cambridge University, U.K. 1982) 94 K. Huang: Quarks, Leptons and Gauge Fields (World Scientific Publ. Co., Singapore
1982) 95 E. Leader, E. Predazzi: Gauge Theories and the New Physics (Cambridge University
Press, Cambridge, u.K. 1982)
444 References
96 P. Goldreich, S. Weber: Astrophys. J. 238,991 (1980) 97 W. Hillebrandt: In 11th Texas Symposium on Relativistic Astrophysics, Dec. 1982 (to
appear) 98 W. Hillebrandt: Astron. Astrophys. 110, L 3 (1982) 99 J. Kirk, J. Trumper: In Accretion Driven X-ray Sources, ed. by W.H.G. Lewin, E.P.1.
van den Heuvel (Cambridge University Press, U.K 1983) 100 S.l. Syrovatskii: Ann. Rev. Astron. Astrophys. 19, 163 (198 I) 101 AG. Pacho1cyk: Radio Astrophysics (Freeman 1970) 102 P. Goldreich, W.H. Julian: Astrophys. J. 157,869 (1969) 103 R.N. Manchester, J.H. Taylor: Pulsars (Freeman, San Francisco 1977) 104 W. Sieber, R. Wie1ebinski (eds.): Pulsars, IAU Symposium No. 95 (Reidel,
Dordrecht 1981) 105 F.C Michel: Rev. Mod. Phys. 54, I (1982) 106 M Abramowitz, l.A Stegun: Handbook of Mathematical Functions (Washington:
NBS 1964) 107 K Nomoto, S. Tsuruta: Astrophys. J. 250, L 19 (198 I) 108 MB. Richardson et a!.: Astrophys. 1. 255,624 (1982) 109 E.H. Gudmundsson: Thesis (University of Copenhagen 1981) 110 P.O. Mazur: 1. Phys. A Math. Gen. 15,3173 (1982) III S. Chandrasekhar: The Mathematical Theory of Black Holes (Oxford University
Press 1983) 112 E. Muller, W. Hillebrandt: Astr. Astrophys. 80, 147 (1981) 113 P.C Joss, S.A Rappaport: In Accretion Driven X-ray Sources, ed. by W.H.G. Lewin,
E.P.l van den Heuvel (Cambridge University Press, u.K. 1983) 114 S. AyasIi, P.C Joss: Astrophys. J. 256,637 (1982) 115 P. Giannone, A Weigert: ZS. f. Ap. 67,41 (1967) 116 CT. Bolton: Astrophys. J. 200,269 (1975) 117 M Oda: Space Sci. Rev. 20,757 (1977) 118 D.R Gies, CT. Bolton: Astrophys. J. 260,240 (1982) 119 B. Paczynski: Astron. Astrophys. 34, 161 (1974) 120 B. Margon et a!.: Astrophys. J. Lett. 185, L 113 (1973); 1. Bregman et a!.: Astrophys.
J. Lett. 185, L 117 (1973) 121 H.A Hill, RT. Stebbins: Astrophys. 1. 200,471 (1975) 122 R Hellings: Talk given at the 10th Intern. Conference on General Relativity and
Gravitation, Padova, July 1983; R. Hellings et aI.: Phys. Rev. Lett. 51, 1609 (1983); Phys. Rev. D 28, 1822 (1983)
123 HA Hill et a!.: Phys. Rev. Lett. 49, 1794 (1982) 124 Ml Rees: Ann. N.Y. Acad. Sci. 302, 613 (1977); Phys. Scripta 17, 193 (1978);
In Origin of Cosmic Rays, IAU Symposium 94, ed. by G. Setti, A. Wolfenda1e (D. Reidel, Dordrecht 1980)
125 AC Fabian, M.J. Rees: In X-ray Astronomy, ed. by W.A Baity, L.E. Peterson (Pergamon 1979)
126 RF. Mushotzky: In 11th Texas Symposium on Relativistic Astrophysics, (Dec. 1982) 127 AP. Lightman: Space Science Reviews 33, 335 (1982) 128 H Bondi: Mon. Not. Roy. Astron. Soc. 112,195 (1952) 129 l.D. Novikov, KS. Thorne: In Black Holes, ed. by C. De Witt, B. De Witt (Gordon
& Breach, New York 1973) 130 A W. Gillman, RF. Stellingwerf: Astrophys. 1. 240,235 (1980) 131 W. Brinkmann: Astron. Astrophys. 85, 146 (1980) 132 L.D. Landau, E. M Lifshitz: Quantum Electrodynamics (Pergamon Press 1982) 133 W.J. Karzas, R. Latter: Astrophys. 1. Supp!. 6, 167 (1961) 134 S. Maxon: Phys. Rev. AS, 1630 (1972) 135 1.R. Ipser, RH. Price: Astrophys. J. 255,654 (1982); Astrophys. 1. 267,371 (1983) 136 J. Schmid-Burgk: Astrophys. Space Science 56, 191 (1978) 137 KS. Thorne: Mon. Not. Roy. Astron. Soc. 194,439 (1981)
References 445
138 K.S. Thorne, RA Flammang, AN. Zytkow: Mon. Not. Roy. Astron. Soc. 194,475 (1981)
139 L. Maraschi, R Roasio, A Treves: Astrophys. 1. 253,312 (1982) 140 RZ. Yahel: Astrophys. 1. 252,356 (1982) 141 D. Freihoffer: Astron. Astrophys. 100,178 (1981) 142 C.F. von Weizsiicker: Z. Naturforsch. 3a, 524 (1948) 143 R Liist: Z. Naturforsch. 7 a, 87 (1952) 144 K.H. Prendergast, G.R Burbidge: Astrophys. 1. Lett. 151, L 83 (1968) 145 N.l. Shakura: Astron. Zh. 49, 921 (1972) 146 1.E. Pringle, M Rees: Astron. Astrophys. 21, 1 (1972) 147 N.I. Shakura, RA Sunyaev: Astron. Astrophys. 24,337 (1973) 148 J.P. Cox, R T. Giuli: Principles of Stellar Structure, Vols. I, II (Gordon & Breach,
New York 1968) 149 R Hoshi: Suppl. Progr. Theor. Phys. 70,181 (1981) 150 N. Straumann: Helv. Phys. Acta 49,269 (1976) 151 RA Sunyaev, J. Trumper: Nature 279, 506 (1979) 152 P.L. Nolan, 1.L. Matteson: Astrophys. 1. 265,389 (1983) 153 P.L. Nolan et al.: Astrophys. 1. 246,494 (1981) 154 AA Galeev, R Rosner, G.S. Vaiana: Astrophys. J. 229,318 (1979) 155 V.M Vasyliunas: Space Science Reviews 24,609 (1979) 156 P. Ghosh, F.K. Lamb: Astrophys. 1. 232,259 (1979); Astrophys. J. 234,296 (1979) 157 F. Meyer, E. Meyer-Hofmeister: Astron. Astrophys. 106,34 (1982) 158 N.l. Shakura, RA Sunyaev: Mon. Not. Roy. Astron. Soc. 175,613 (1976) 159 D. Page, K.S. Thorne: Astrophys. 1. 191,499 (1974) 160 MA Abramowicz, M Jaroszynski, M Sikora: Astron. Astrophys. 63,221 (1978) 161 M Koslowski, M Jaroszynski, M.A. Abramowicz: Astron. Astrophys. 63,209 (1978) 162 B. Paczynski, P. Wiita: Astron. Astrophys. 88,23 (1980) 163 B. Carter: In Active Galactic Nuclei, ed. by C. Hazard, S. Mitton (Cambridge
University Press, u.K. 1979) 164 K.S. Thome, D. Macdonald: Mon. Not. Roy. Astron. Soc. 198,339 (1982) 165 D. Macdonald, K.S. Thorne: Mon. Not. Roy. Astron. Soc. 198.345 (1982) 166 L.D. Landau, E.M Lifschitz: Fluid Mechanics (Pergamon 1959) 167 PA Thompson: Compressible-Fluid Dynamics (McGraw-Hill 1972) 168 G.K. Batchelor: An Introduction to Fluid Dynamics (Cambridge University Press
1967) 169 T. Damour: In Gravitational Radiation, ed. by N. Deruelle, T. Piran (North-Holland
1983) 170 T. Damour: Talk given at the 10th Intern. Conference on General Relativity and
Gravitation, Padova, July 1983 171 AL. Fetter, J.D. Walecka: Quantum Theory of Many-Particle Systems (McGraw-Hill
1971)
Subject-Index
Absolute derivative, see Covariant derivative
Absolute exterior differential 65 Acceleration 113, 118, 120
see also Fermi-transport; Geodesic deviation
Accretion as source of x-rays from compact ob-
jects 201,378,382,388 in x-ray binary pulsars 377-378 in x-ray binary bursters 380 onto black holes and neutron
stars 388 ff tori 432 see also Spherical accretion onto black
holes; Disk accretion Accretion rate 378, 388, 391
critical 414 Action
Einstein-Hilbert 148 principle ofleast, see Variational prin
ciple Adiabatic index 280,337-338
critical value for radial stability 337-338
during supernova formation 337 Affine connection 47
curvature of 54 induced 47 metric 57,63 torsion of 54
d' Alembertian 95 Alfven radius 377 Alternation operator 27 Angular momentum
of black holes 363 of isolated systems 156-157
Antiderivation of differential forms 30 Asymptotically flat space-time 154
angular momentum of 156 f, 230 ff energy and momentum of 146, 154fT,
229ff
Asymptotic fields in post-Newtonian approximation 252 of isolated systems 229 of Kerr-Newman black holes 362-363
Atlas 4 differentiable 5 maximal 5 oriented 36
Autoparallel along curve 49
Background geometry 217 Basis
ofp-forms 28 of tangent space 13 of vector space of derivations 11 oriented 39
Bernoulli equation 390,393,435 nonrelativistic 435 relativistic 390
Beta-equilibrium 294-295 and Urca process 313 for ideal mixture 295
Bianchi identities 56, 60, 64, 66, 73 as constraint equations 161 contracted, reduced 60-61, 128, 132,
152 derivation and meaning of 138-139 linearized 214
Binary pulsar PSR 1913+ 16 240,258, 261,264,266 advance of periastron 268 arrival time data 266
analysis of 267 change of period 268
and gravitational radiation 240,270 and viscous dissipation 276
companion 271-276 mass of 269
discovery 266 dispersion measure 267 distance 267 important parameters 268-269
448 Subject Index
Binary pulsar PSR 1913 + 16 mass 269 orbital period 266 orbital phase shift 270 pulse period 266 relativistic effects 268 self-consistency of post-Newtonian
parameters 270 spin precession 264, 269
Binary x-ray pulsars, see X-ray binary pulsars
Binary x-ray sources, see X-ray binaries Birkhofftheorem 169, 198
generalized 2 I 1 Black holes
angular momentum parameter 363 approach to stationary state 361,372 area of horizon 369 charge of 363 Cygnus X-I 372,382 effective potential for test particle 174,
176 ergosphere 366 extraction of rotational energy 368 g-factor 364 horizon 197,200,367-368 identitying compact objects as 201,299,
372,382,385 inevitability of collapse to black
hole 82, 189 Kerr 362 Kerr coordinates 367 Kerr-Newman 362 Kruskal coordinates 193,195,197 miniholes 369 naked singularity 365 "no hair" theorem 361,372
special cases 362 nonrotating ("Bardeen") observers 365 parameters for stationary solutions 362-363 Reissner-Nordstmm 172,207 rigid rotation of horizon 366 rotating 361, 363 Schwarzschild 169, 195ff, 200-201 singularity 197,200,367 spontaneous radiation of 369 trapped surface 371 see also Accretion on black holes; Gravi
tational collapse; Kerr-Newman metric; Schwarzschild; ReissnerNordstmm solution
Bremsstrahlung 397,408 absorption coefficient 408 electron-electron 398 electron-ion 397-398
spectral emissivity 397 total emissivity 398
Cartan calculus 27 Cauchy data 160, 162-163 Cauchy development 160
local existence 161-162 stability of 371
Cauchy Lemma 433 Cauchy problem 160 Cauchy surface 160 Cauchy traction 433 Causal structure 171,192, 195ff Chain rule 10 Chandrasekhar limit 283,329,337,341,
346 historical remarks 283
Characteristic surfaces ofa differential equation 164 of Einstein's field equations 163 ff of Maxwell's vacuum equations 165 of the generalized wave equation
163-164 Chart 4
domain of 4 positive 36
Christoffel symbols 48,61,90 along a path 118 transformation law for 48
Class Coo 5 differentiable manifold 5 function on manifold 6 function on R n 5 mapping 6
Codazzi-Mainardi equation 162 Codifferential 40, 42, 46, 72, 94
coordinate expression of 40, 72 Compact x-ray sources, see X-ray binaries Comptonization 408 Conductivity
electrical 349, 380 thermal 308
Conformal invariance of scalar wave equation 95 of source-free Maxwell equations 95
Conformally flat manifold 87 theory 134
Conformal metrics 94 Congruence of time like geodesics 124 Cooling of neutron stars 305 ff
comparison with observations 320 cooling curves 318-321 early versus late phases 305-306 effects of general relativity 319
neutrino emissivities 313 observations 306 role of magnetic fields 319 specific heat 312 temperature distribution 308
Cooling time 318 role of pion condensate 319,321 see also Neutron stars; Neutrino emission
from neutron stars Coordinate representation
of codifferential 40, 72 of covariant derivative 54, 72 of differential form 29 of exterior differential 33 offunction 12 of Lie derivative 25,71 of star operation 38 of tangent mapping 13 of tensor field 15 of vector field 15
Coordinate transformation 5 infini tesimal 216
Coordinates 4 change of 5 Eddington-Finkelstein 198 ff for Schwarzschild solution, see
Schwarzschild Gaussian 50 harmonic 161,228 local 12 normal 50, 130 ofa point 4 singulari ty 171, 190 traceless transverse (TI) 224
Commutator of derivations 16 of vector fields 16,24,71
Complete tensor algebra 24 vector field 22
Components of affine connection 48 of differential forms 30 of tensor field 18 of vector field IS transformation law of 15, 18
Connection coefficients 48 see also Connection forms
Connection forms 61,72, 147, 162,209 ofa spherically symmetric field 167
209 transformation properties of 65, 147
Conservation law, associated to a Killing field 146,
174
Subject Index 449
of angular momentum 156-157 of electromagnetic current 93 of energy and momentum 91,154ff
Copernical frame III, 116 rotation ofa 116
Core collapse 281,330,338 adiabatic nature 344, 348 conditions at onset of 280, 345 core bounce 342, 347 dynamical time scale 344 dynamics of collapse 338 entropy generation during collapse 342,
344, 348 homologous core mass 341 homologous nature 338-341 inevitability of collapse 337 models of type II supernovae 330 neutrino trapping 342-344 neutronization 342, 345 neutronization as trigger 337,341 persistence of heavy nuclei 344 photo dissociation as trigger 280,
337-338 see also Supernova formation
Coriolis force 121 Cosmic censorship conjecture 201,371 Cosmological constant 133-134 Cotangent space 17 Covariance
general 88 with respect to K(M) 88, lSI
Covariant derivative 49 along a curve 49 and exterior derivative 35 and parallel transport 50, 52 as a derivation of the tensor algebra 52 local expression of 54, 72 of tensor fields 51,53 of vector fields 49
Covariant tensor algebra 23 field 20
Crab nebula 281,354-355 energy spectrum of electrons in 354 magnetic fields in 354 synchrotron lifetime of
electrons 354-355 synchrotron radiation from 354
Crab pulsar 281, 306, 353-355 Curvature forms 62, 73
dual 153 ofa spherica!Jy symmetric field 168,
210 transfonnation properties of 66, 147
Curvature of affine connection 54
450 Subject Index
Curvature tensor 54 components of 55 physical meaning of 123 ff symmetry properties of 58, 60
Curve covariant derivative along 49 differentiable 21 geodesic 50 integral 21 maximal integral 21
Cyclotron line spectroscopy 348-349 Cygnus X-I 202,372,374,382,388
as a black hole candidate 202, 382, 385 distance 384 general properties 382-383 likely mass 385 lower limit to mass 383-385 luminosity 382 mass function 383 optical companion 382 orbital parameters 382-383 time variability 382 x-ray spectrum 382
Dark matter in galaxies 297 neutrinos as 297
Debye function 311 Debye heat capacity 311 Debye temperature 311 Deflection of light rays, see Light rays Deformation tensor 432 Domain of dependence 160 Derivation
induced 31 local 30 of algebra of smooth functions 16 of differential forms 30 of function with respect to vector
field 16 of germs off unctions 10 restriction of 31
Diffeomorphism 5, 6 Differentiable manifold, see Manifold Differentiable structure 6, 8
class Coo 5 inequivalent 6 of product manifold 8
Differential of a function 17 ofamap 10 of component functions 18 one-form 19 topology 6
Differential forms 27, 29 antiderivation of 30
closed 33 components of 30 derivation of 30 exact 33 exterior derivative of 32,35,71 induced mapping of 30 interior product of 28-29,71 local basis of 21 tensor valued 65, 73
Dimension of differential manifold 12 of p-forms 28 of topological manifold 12
Disk accretion basic equations for thin disks 401-406
angular momentum conservation 403 energy conservation 404 equation of state 401 equations for vertical structure 405 mass conservation 402 radial momentum conservation 404
early theoretical work 40 I Keplerian disks 406
effective temperature distri-bution 409
efficiency 408 emission spectrum 409-410 luminosity 408 opacity 408 radial structure equations 406 vertical structure equations 407
relativistic Keplerian disks 425 basic equations 425-427 dissipation function 427-429 energy production 430-431 torque equation 429
stability of accretion disks 419 basic equations 420-423 dispersion law 423-424 modes of instability 424-425 sta bility criterion 424
standard disks 410 a-law 411 analytic solutions 414-415 numerical solutions 416-418 radial structure 413 vertical structure for polytropic
equation of state 411 viscosity 410-411
see also Accretion Dissipation function 405,427,435 Divergence of vector field 45 Divergence theorem 46 Doppler shift 108-109
Dual basis 17 in cotangent space 17 of one-forms 61,72 of vector fields 20, 72
Dual space 17 Dual transformation 23 Dyson-Lenard-Lieb-Thirring theorem 323
Eddington-Finkelstein coordinates 198-199
Eddington luminosity 382, 388,414 Eddington-Robertson parameters 182 Effective mass 308,310-311 Einstein 77,87,80 Einstein's field equations 127 ff
characteristics of 163 ff dependence of 139 heuristic derivation 129 in tetrad formalism 140-141 Landau-Lifshitz decomposition of 158 ff linearized 215, 217-218 uniqueness 129 ff
Einstein-Fokker theory 135 Einstein-Infeld-Hoffmann equations 255
Lagrangian for 255 Einstein Observatory 306, 374 Einstein's quadrupole formula 235 Einstein-Rosen bridge 198 Einstein tensor 61, 130,132
linearized 214 of a spherically symmetric
field 168-169,211 Electrodynamics 93-94
analogy with 143-144 formulation with exterior calculus 94f identity as a consequence of gauge in-
variance 139-140, 144 in tetrad formalism 152-153
Electron capture 280, 336, 345 shell-blocking effects 345
Electron fraction 280 of collapsing core 345 of iron-nickel core 280
Embedding 7 Emission of gravitational radiation 233 ff
of a binary system 237 ff Energy and momentum
conservation 91-92, 142, 144 of gravitational waves 234-235, 237 of gravity for isolated systems 154-155 tensor
for system of point particles 252 in geometric optic limit 104 in Lagrangian field theory 141-142
Subject Index 451
in post-Newtonian approxi-mation 253
of electromagnetic field 142-143, 153 of ideal fluid 91 symmetry of 151
three forms 149, 155 total 154
for Schwarzschild solution l70-17l of isolated systems 154 ff
Energy transport equation 307,407 Entropy
during supernova formation 344 flux four-vector 436-438 of iron-nickel core 280,344 per baryon 307,343,436 production 438-439
Eotvos experiment 78 Equation of state
for hot plasma 393,401 for ideal n-p-e mixture 294 general properties 299,309 polytropic 338 realistic equations of state 298, 304,
308,319 Equivalence principle, see Principle of
equivalence Ergosphere 366 Euler equations 434
relativistic 92 Euler-Lagrange equation, see Variational
principle Event horizon 197,200,367-368
see also Black holes Evolution of massive stars 280
acceleration in late phases 334, 337 evolutionary tracks 333 instability of core 280,337,341 leading to degenerate cores 280,337 mass of degenerate core 337 neutrino emission and 280, 334 nuclear statistical equilibrium 333, 338 onion structure 333 pres up ern ova 332 thermonuclear reactions 333
Expansion tensor 439 Exponential mapping 50
and normal coordinates 50 Exterior algebra 28
of differential forms 29 Exterior derivative 32, 35, 71
expression for 35,71 morphisms and 333
Exterior differential forms 29 components of 30 induced mapping of 30
452 Subject Index
Exterior forms 27 Exterior product 27
Fermat metric 110 Fermat's principle 99 Fermi
derivative 113-114, 127 transport 113 ff
Field strength electromagnetic 93
in a static Lorentz manifold 110 gravitational-inertial 90
Fitting procedure of Eckart 439 Flat manifold 68
locally 68 Flow of vector field 21 f
global 22 local 22
Fourier law nonrelativistic 436 relativistic 439
Gap energy in superfluids 311-312 density dependence 312
Gauge group oflinearized theory 215,217 harmonic 162,228
conditions 161,244,247,251 Hilbert 218,220,227 traceless transverse (Tf) 223 transformations 88, 139 transformation in linearized
theory 215-216,218,220-221 Gaunt factor 397 Gaussian coordinates, see Normal coor-
dinates Gauss' formulas for submanifolds 162 Gauss' theorem 45-46 Geodesic curve 50
equation for 50 in local coordinate system 50, 119
Geodesic deviation 125 equation of 125 in a gravitational wave 224
Geometric optics 100 Germ
of paths 14 of smooth functions 10 of smooth mappings 9
Ginzburg-Landau parameter 311 Grassman algebra 28
see also Exterior algebra Gravitational Bohr radius 81 Gravitational collapse
qualitative picture 371-372
spherically symmetric 200 ff see also Black holes; Core collapse;
Supernova formation; Supernovae Gravitational constant 81
change of 186 Gravitational energy, see Energy and
momentum nonlocalizabilityof 146
Gravitational field 90 at large distances from the source 226 ff equation 127 ff external 89 ff geometric optics in a 100 ff spherically symmetric 208-209 static 97-98, 104fT, 115ff, 172 stationary 104 ff, 115 ff weak 96-97, 132, 214 ff
Gravitational fine structure constant 81 Gravitational interaction
strength of 81 universality of 82
Gravitational radiation 233-234 Einstein's quadrupole fornmla 235 from binary pulsar system 240, 270 from binary star system 237 in core collapse 281 of non stationary black hole 361,372 of rotating neutron star 354
Gravitational red shift 83 ff see also Red shift
Gravitational waves in the linearized theory 220 ff energy flux of 234-235,237 geodetic deviation in 224 see also Einstein's field equations;
Energy and momentum
Hadronic neutral current 342 Hamilton's Principle, see Variational prin-
ciple Hawking's area theorem 369f Heat conduction 307 Heat flux four-vector 438 Helicity 222 Helium flash 381 Hercules X-I 348,374,377-378
cyclotron line 349 magnetic field 349 optical companion 377 pulsation and orbital periods 374 x-ray spectrum 349
Horizon for Kerr-Newman metric 367-368 for Schwarzschild metric 171, 197,200-201 see also Black holes
Hydrodynamics of viscous fluids for perfect fluid 92 nonrelativistic theory 432
continuity equation 433 decomposition of velocity
gradient 432 different forms of energy
equation 434-435 equations of motion 434 substantial derivative 432 transport theorem 433
relativistic theory 436 energy balance equation 439 energy-momentum tensor 440 entropy production 438-439 equilibrium 436 relativistic Fourier law 439 relativistic Navier-Stokes
equation 440 small departures from
equilibrium 437
Ideal fluid 91 conservation of energy-momentum
tensor of 144 spherically symmetric solution
for 212-213 static field of 129 see also Euler equations; Hydrodynamics
of viscous fluids Immersion 6 f Induced
algebra homomorphism 10 derivation 31 mappings 23, 30 orientation of boundary 44 Riemannian metric 46 scalar product 38
Inertial system global 86 local 83,89, 147
Infinitesimal transformation 24 Integral curve of vector field 21 Integration of differential forms 42-43 Invariant tensor field 24 Isolated systems 154 ff
see also Angular momentum; Energy and momentum
Isometry 68 infinitesimal, see Killing field
Jacobian of mapping 12 Jacobiequation 125 Jacobi field 125
Subject Index 453
Kerr-Newman metric 362 asymptotic field 363 Boyer-Lindquist coordinates 362, 364 coordinate singularity 367 horizon 366,368 Kerr-coordinates 367 special cases 362 structure of light cones 367 see also Killing fields
Killing equation 105, 146 Killing fields 104 if, ll5 ff
for Kerr-Newman metric 364 for Schwarzschild metric 174,192-193
Komar formula 232 Kruskal
continuation of Schwarzschild solution 190ff
coordinates 193,195,197,200 diagram 196,200 transformation 195 see also Schwarzschild; Black holes
Lagrange point 376 Lagrangian formalism l35 ff
density, of matter fields 140 invariance properties of 150-151 of the electromagnetic field 140 relative to an orthonormal basis 153 total 149
for a test particle in a Schwarzschild field l37ff
for the linearized theory 217 Landau-Lifschitz three forms, see Pseudo
tensors Landau parameters 310,315 Laws of physics in external gravitational
fields 89 ff Leibniz rule 10, 30 Lense-Thirring effect 263, 265
see also Precession of gyroscope Levi-Civita connection 58
local expression of 58 Lie algebra of vector fields 17,71 Lie derivative 21,24,71
local coordinate expression of 25,71 of metric tensor l39
Lie transport llS, 124-125 Light rays
deflection of 86 by the solar corona 181-182 in a Schwarzschild metric 178 ff measurements of 180-181
in geometrical optics 103 paths of 90
Linear connection, see Affine connection
454 Subject Index
Linearized Bianchi identities 214 Linearized Einstein tensor 214 Linearized field equations 215,217-218 Linearized field, multipole expansion
of 226ff Linearized Ricci tensor 214,217 Linearized Riemann tensor 223 Linearized theory
gravitational waves in 220ff of gravity 214ff
Local basis of one-forms 21 of vector fields 21
Local coordinate neighborhood 4 Local coordinate systems 12, 118-119 Local flow of vector field 21 Local inertial system 83,89, 147 Local Lorentz transformation 147, 151 Locally finite covering 43 Local one-parameter group 22 Local reference frames 111 ff Lorentz gauge condition 102 Lorentz invariance, local 151 Lorentz manifold 88
spherically symmetric 88 see also Manifolds, Pseudo
Riemannian Lorentz transformation 147
local 147, 151
Magnetic dipole radiation 352 see also Pulsars
Magnetic fields conservation of magnetic flux 350 determined with cyclotron line 348-349 diffusion time 350 infl uence on neutron star cooling 319 matter in strong magnetic
fields 358-360 of neutron stars 348-349,353 rapid dissipation 350 reconnection 350 relativistic magnetohydro-
dynamics 351-352 Magnetosphere of pulsar 355-358 Manifold 4 ff
differentiable 6 dimension of 12 flat 68 locally flat 4 orientable 36 oriented 36 paracompact 4 product 8 (pseudo-)Riemannian 20
Sch warzschild -Kruskal 196 sub- 7 open 5 a-compact 4 topological 4, 12
Mappings and tensor fields 22 coordinate representation of 6 differentiable 6 of class Coo 5-6
Mass function for binary systems 382 Material derivative 432 Matter in strong magnetic fields 358-360
ground-state energy of hydrogen atom 360
Maximal mass of neutron stars 300 for realistic equations of state 298 model independent bounds 299, 305
Maxwell's equations 93 as variational equations 144 characteristics of 165 conformal invariance of 94
Mean free path and diffusion constant 343 of neutrino during supernova
formation 342 of neutrino in neutron star 307
Measure-valued one-form 45 Mechanics of binary systems 374-376,
382-383 mass function 382 motion oftest particle 375
equilibrium positions 375 equipotential surfaces 375 Jacobi integral 375 inner Lagrange point 376 nature of critical points 376 Roche lobe 376
Navier-Stokes equation in corotating system 376
velocity curve 383 Melting temperature of ion lattice 310 Metric
conformally flat 134-135 connection 57, 63 Lorentzian 88 physically equivalent 139 pseudo-Riemannian 19 raising and lowering indices with 59 Riemannian 19 see also Kerr-Newman metric; Post-New
tonian approximation; Schwarzschild metric; Weak field approximation
Mini-black holes 369 Motion ofa test body, see Test body
Moving frame 61 see also Tetrad field
Mobius strip 36 Multilinear forms 27 Multilinear mapping
associated to tensor field 19 differential forms 29
Multipole expansion of linearized field 226ff
Naked singularity 365 Navier-Stokes equation
nonrelativistic 434 relativistic 426, 440
Neutral current interaction 313 and neutrino scattering 342 effect in pair annihilation 335-336 effective four-fermion interaction 314,
342 Neutrino emission
from neutron stars gradient of neutrino luminosity 307 influence of super fluidity 318 modified Urca rate 314-316 modified Urca reactions 313 neutrino pair bremsstrahlung 313 neutrino transparency 307 nucleon pair bremsstrahlung 313 pion condensate ,B-decay 317 suppression ofUrca reactions 313 see also Cooling of neutron stars
from supernovae 305 neutrino trapping 342-344 neutronization reactions 342 thermal reactions 305, 334, 345 see also Supernova formation; Core
collapse of massive stars 334
important processes 334 luminosity 333, 336 pair annihilation 334-336
Neutrino opacity 342 Neutrino scattering
on heavy nuclei 342-343 on neutrons 343
Neutrino stars 297 Oppenheimer-Volkofflimit for 297
Neutrino trapping 342-344 Neutronization 280
see also Electron capture Neutron stars 280 ff
allowed core region 302 and supernovae 281,285,306,346 bounds for mass 189,305 central core 294
Subject Index 455
cooling of, see Cooling of neutron stars crust 293-294 cyclotron lines 348-349 density profile 298 detailed models 297 equations of state 297 Fermi momenta of nucleons 309 formation 281,285,346 gross features 285 historical remarks 285 hyperons in 294 ideal n-p-e model 394 inner fluid 294 interior 293 magnetic fields 348-349, 353 mass-radius relation 297 maximum mass 296,298-299,305 observations
comparison with cooling calcu-lations 318-321
cyclotron lines 348-349 masses 269, 379 radii 381 surface temperatures 306 thermal radiation 306 see also Binary pulsar; Pulsars; X-ray
binary bursters; X-ray binary pulsars
Oppenheimer-Volkoffmodel 296 pion condensate 294, 316 quark phase in 294 relation between surface and interior
temperature 308 specific heat 308, 312 supercond uctivity in 294, 311 superfluidity in 294,310,318 temperature profile 308 thermal energy transport 307 thermal equilibrium 306-307 thermodynamic properties 306 ff uniform density model 290, 318 see also Accretion; Binary pulsar:
Pulsars, Superfluidity in neutron stars; Supernovae; Binary x-ray sources
Newtonian limit 96-97, 133 potential 126, 128 theory, comparison with 126
Newton vs. Coulomb 327 Nonsaturation of gravitational forces
heuristic discussion 324 rigorous results 325-327
Normal coordinates 50 Nova outbursts 387 Nuclear density 295,310
456 Subject Index
Nucleon-nucleon interaction BCS pairing 311-312 in nucleon pair
bremsstrahlung 314-315 Landau interaction 316 Landau limit 316 one pion exchange 315 short range contribution 315
Number density of baryons 289,307
Observer at rest 107 rotation of 120
One-forms 19 covariant derivative of 53 pull back of 19
One parameter group local 22 of diffeomorphisms 22
Opacity 307,408 electron scattering 408 free-free transitions 408 Rosseland-mean 408
Orientation and volume forms 36 induced 44 of boundary 44 of manifold 36 same 36
Oriented atlas 36 Oriented basis of one-forms 39 Oriented manifold 36
Palatini identity 217 Parallel transport 50-51
path independence of 69 Penrose mechanism 368 Perihelion (periastron)
advance of 176fT, 220, 258, 268 of mercury 178
see also Binary pulsar; Post-Newtonian approximation
Perturbations adiabatic 291,338 eigenvalue equation for 291 of thin accretion disks 419
Photodisintegration 280 of iron-nickel core 280,337-338
Photospheric boundary conditions 307 Pion condensation 294,316
chiral rotation 317 influence on neutron star cooling 306,
318,320 quasiparticles in presence of 317 wave vector 317
Planetary orbits 273 ff Plane waves in the linearized theory 221 ff
polarization states of 222 polarization tensor of 221
Plasma frequency 310 Poincare Lemma 33,40,71 Polarization
states of gravitational waves 222 tensor for the linearized field 221 vector of electromagnetic waves 10 1
Positive chart 36 Positive coordinate system 37 Post-Newtonian approximation
asymptotic fields 252 Christoffel symbols 248 equation of motion 255 field equations 246 gauge conditions for 244,247,251 metric 254 periastron shift 258 precession of gyroscope 261 Ricci tensor 245 two-body problem 256
center of mass in 256 Hamilton-Jacobi function of 260 Hamiltonian for 257-258 Lagrangian for 256 solution of 258
Post-Newtonian potentials 247 for system of point particles 254 particle in 249
Langrangian for 249 Potential
gravitational inertial 88 effective 174, 176 electromagnetic 93 ff Newtonian 126, 128,219
Precession of gyroscope geodesic precession 186 ff, 263, 265 in a gravitational field Iliff, 115 in a Schwarzschild field 186ff in orbit around the Earth 263 in post-Newtonian
approximation 261-263 Lense-Thirring effect 263, 265
Principle of equivalence 79, 81 ff, 135 ambiguities 95 mathematical formulation 87
Principle of general covariance, see Covariance
Product manifold 8 differentiable structure of 8
Pseudo-Riemannian manifold 20 Pseudo-Riemannian metric 19
Pseudotensors and three-forms of stressenergy for gravitational field 155 Landau-Lifschitz 155-156
for a plane wave 236-237 see also Energy and momentum; Super
potential Pull back
of covariant tensor field 20, 22 of one-form 20
Pulsars aligned rotator model 355, 357 as rotating neutron stars 352 braking index 353 characteristic age 353 energy in radio pulses 354 gravitational radiation from 354 induced electric fields 355, 357 instability of exterior vacuum solu-
tion 355-357 light cylinder model 358 magnetic dipole radiation 352-353 magnetic fields 353 magnetospheres 357 periods 352 polar cap model 357 radius oflight cylinder 357 spindown 352-353 see also Binary pulsar; Crab pulsar;
Supernovae
Quadrupol formula for radiation 235 moment of the Sun 177-178 oscillations in gravitational waves 225 tensor 234
Quasars 388 see also Supermassive black holes
Quasiparticles 308,317-318
Radau equation 272 Rank of differentiable mapping 14 Rapid Burster 382 Red shift 83,85,97,108
and temperature distribution 307 experiment 84 from source at static limit 365 gravitational 83-84 in a static gravitational field 97-98 in Schwarzschild field 22 ff inconsistency between SR and gravi-
tational 85-86 Region 44 Reissner-Nordstrom solution 172,207 Related vector fields 23 Relativistic enthalpy 301,390,426
Subject Index 457
Ricci identity 57 Riccitensor 60,73
linearized 214,217 Riemannian
connection 58 curvature tensor 54
linearized 223 manifold 20 metric 19
Roche lobe 376 Rotating black holes 361 ff
see also Black holes, Kerr-Newman metric
Rotational distortion 273 Rotation of a Copernican system 116
Scalar curvature 128, 136-137, 148 Schwarzschild field, test-particle motion
in 173 ff curvature forms of 168 geodetic precession in 186 ff
Schwarzschild-Kruskal manifold 196 Schwarzschild metric, geometric meaning
of 171-172 in harmonic coordinates 229 Killing fields for 174,192-193
Schwarzschild radius 171 Schwarzschild solution 169, 196
derivation of 166 ff in Eddington-Finkelstein coor-
dinates 198ff in Schwarzschild coordinates 169 in nearly Lorentzian coordinates 170 Kruskal continuation of 190ff stability of 207 total energy and momentum of 170-171
Schwarzschild throat 198 Semirelativistic systems 329 Shear tensor 439 Singularity
of coordina te systems 171, 190 theorem 371 true 197
Sirius B 283 Specific heat
of crust 310 of normal Fermi liquids 308 of super fluid nucleons 310
Spherical accretion onto black holes adiabatic flow 389 critical point 392 density and temperature profiles 396 justification for hydrodynamical de-
scription 399-400 magnetic fields 399
458 Subject Index
Spherical accretion onto black holes non-adiabatic 400 thermal bremsstrahlung 395,398-399
efficiency 399 spectrum 399
transsonic accretion rate 394 transsonic flow profile 395 see also Accretion
Spin precession in a Schwarzschild
field 186ff precession of III ff rotation in a stationary field 117
Spin-tensor 432 Stability
changes at critical points 291 of accretion disks 419 of macroscopic matter 321 ff of spherically symmetric stars 290-291,
338 role of general relativity 337
Star operator 37-38,72 Static gravitational field 97-98, 104ff,
115 ff, 172 Static limit, see Black holes Stationary gravitational field 104 if, 115 ff Stellar evolution
in binary systems 386 qualitative picture 281 ff see also Evolution of massive stars
Stellar structure Newtonian compared with general re
lativistic 298, 306-307 relativistic equations 286, 289 stability 290
and critical points 291 linear analysis 290, 338
thermal energy transport 307 thermal equilibrium 306-307
Stokes' theorem 44 Stress tensor 434
viscous 434 Structure equations 62f, 73
solution of 63 Submanifold 7
open 5 regular 7 totally geodesic 163
Superconductivity in neutron stars 311 f Superfluidity in neutron stars 294, 310
and neutrino processes 318 effect on specific heat 310 gap energies (s-, p-waves) 312 recombination of Cooper pairs 318 transition temperature 312
Supermassive black holes 202, 388, 399, 409 as quasar model 388
Supernovae and neutron star formation 281, 285,
306,346 association with pulsars 285, 306 energy released 332 formation
core bounce 342, 346-347 damping of shock 345 energy released 332 entropy generation during col-
lapse 342,344,348 neutrino trapping 342-344 neutronization as trigger 337,341 numerical studies 344-347 onset of collapse 280,337,345 persistence of heavy nuclei 344 photo dissociation as trigger 280,
337-338 physics of collapse 338ff production of shock wave 342,
344-347 propagation of shock wave 346-347 strength of shock 345,347 see also Core collapse; Neutrino
emission from supernovae; Supernovae
historical 306, 330 neutronization as trigger 337,341 observational facts 330-332 photodisintergration as trigger 280, 337 rate 331 type I versus type II 331
Superpotential 159 Synchrotron radiation from Crab
nebula 354
Tangent map 10,14 Tangentspace 9,10,13-14
algebraic definition 10 canonical isomorphisms 13-14 geometrical definition 14 physicist'S definition 13
Tangent vector 14 Tensor fields
algebraic operations on 18 components of 18 covariant 20 invariant 24 of class cr, Coo 18 of type (r, s) 18 tensor product of 18 traceless transverse (TI) 223
Tensor valued forms 65, 73
Test body in a Schwarzschild field 173 ff in a weak gravitational wave 224-225 motion of 90,120-121
Tetrad field 61, 147 orthonormal 147 transformation of 147 variation of 148
Tetrad formalism 147 ff Thomas precession 112-113 Tidal distortion 270 ff Tidal forces 12, 123, 126
on surface of a collapsing star 204 ff Time delay of radar echoes 182 ff
caused by the solar corona 185 Time-orientable 88 Tolman-Oppenheimer-Volkoff (TOV)
equation 288,292, 300 Topological manifold 4
dimension of 12 paracompact 4 a-compact 4
Torsion forms 62 transformation properties of 66
Torsion of affine connection 54 Torsion tensor 54 Transport theorem 433· Trapped surface 371
formation 371 stability of phenomenon 371
Uhum x-ray satellite 373-374 Urca reactions, see Neutrino emission from
neutron stars Universality of gravitational inter
action 82
Variational principle for light rays 99-100 for matter fields 140-141
Euler-Lagrange equations 141 for the coupled system 145 for vacuum field equations 136
Variation of the metric 137-138 of the tetrad fields 148 of the vector potentials 143 of the volume form 141
Vector fields 15 algebraic operations of 16 as derivations 16 commutator of 17 complete 22 components of 15 derivation associated to 16 derivative with respect to 16
Subject Index 459
divergence of 45 flow of 21 integral curves of 21 Lie algebra of 17, 7 I Lie bracket of 17, 24, 71 of class Cr, Coo 16 related 23
Vela pulsar 281 Vierbein, see Tetrad field Virial theorem 28 I Viscosity 389,410,416-417
bulk 434 for standard disks 4 I 6 kinematic 420 radiative 416 shear 434
Volume element 36-37,45,72 and associated measure 136 and orientation 36 corresponding to metric 37
Volume expansion 439 Vorticity tensor 439
Weak gravitational field 96-97, 133, 2l4ff White dwarfs 284, 330-332
X-ray binaries discovery 374 disk and wind accretion 378 optical companions 377,379 origin and evolution 386 see also Accretion; Cygnus X- I; X-ray
bursters; X-ray binary pulsars X-ray binary pulsars 377-379
discovery 374 magnetic fields 348, 377 mass flow rates 378 masses 379 size of magnetosphere 377 size of radiating polar cap 377 temperature of hot spots 377 x-ray luminosities 377 see also-Accretion; X-ray binaries
X-ray bursters 379ff discovery 374 evidence for disk accretion 380-381 general properties 380 location in old stellar populations 380 optical companion 374 optical echo 38 I radii 381 rapid burster 382 thermonuclear flash model 380-381 see also Accretion; X-ray binaries
Zeroth law of gravitation 127
