# Antigravity and Maximal Acceleration

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<ul><li><p>Annnlen der Physik. 7. Folge, Band 47, Heft 8, 1990, S. 677-678 J. A. Barth, Lcipzig </p><p>Short Communieaiion </p><p>Antigravity and Maximal Acceleration </p><p>By CORRADO MASSA </p><p>Reggio Emilia, Italy </p><p>Antigravitation und maximale Beschleunigung </p><p>Attempts to unify gravitation with the other natural forces suggest [l] gravity is transmitted by a particle of nonzero rest mass m in addition to the usual maasless gravi- ton. If so, the gravitational potential V(r ) of a mass M contains a component of the Yukawa form and reads </p><p>V ( r ) = a ( W r ) + B(M/r) exp(-pr) , (1) where a, f i are (respectively) the coupling constant of the massless and of the massive graviton; = mc/ti is the inverse Compton wavelength of the massive graviton (c = the speed of </p><p>light, ti = the reduced Planck constant). At small distances, pr + 0 and V ( r ) 4 -GM/r where G = -(a + B) is the gravitational constant, measured locally (a- 6.67 10-8 cm3 g-1 s-%). Eq. (1) can be written as </p><p>V ( r ) = - (GM/r) (1 + b)-I [l + b exp(-pr)], b # 1. </p><p>The gravitational acceleration r = a = --dV/dr is </p><p>a = - (GM/r*) (1 + b)-l[ 1 + b( 1 + X) exp( -X)] , X = pr . </p><p>(3) </p><p>Any mass m, placed at rest at the distance r from M obeys the relativistic-qimntum constraint [ 21 </p><p>la1 &lt; 2 m0c3/h. (4) </p><p>The numerical value and the sign of b depend on the particular theory involved. Assume b &gt; 0 and obtain from (5) </p><p>b &lt; (1 - y+)[y? - (1 + X) exp(-X)]-l. (6) </p></li><li><p>678 Ann. Physik Leipzig 47 (1990) 8 </p><p>As r 03, the constraint is obeyed only if b &lt; - 1, in contrast with our assumption b &gt; 0; therefore we must drop the assumption b &gt; 0 and are forced to conclude b &lt; 0 (if b # 0, of course). </p><p>I dont investigate the case r + 0 because as r + 0 the quantum spread in the linear momentum of m,, tends to infinity and our zero-initial-speed assumption breaksdown. </p><p>A negative b means that gravity is a mixture of the ordinary attractive force, carried by the spin-2 graviton, and of a repulsive force (antigravity); thus our result b &lt; 0 implies the massive graviton is a spin-s particle with 8 = an odd number, likely 1 (of course on scale larger than l/p the antigravity component is negligible and attraction dominates). Its interesting to point out antigravity arises naturally in supergravity theories . Notice also the assumptions b - -0.9 and 1/p- 1P cm (= a typical galactic size) explain the observed flat shape of the galactic rotation curves with no need of postulating the presence of dark matter. </p><p>References </p><p>[l] GIBBONS, G. W.; WHITINQ, B. F.: Nature, 291 (1981) 636.  CAIASIELLO, E. R.: Lett. Nuovo Cimento 41 (1984) 370, and references therein.  SHERK, J.: Phys. Lett. 88 B (1979) 266.  SANDERS, R. H. : Astron. Astrophye. 186 (1984) L 21. </p><p>Bei der Redaktion eingegangen am 2. Februar 1990. </p><p>Anschr. d. Verf.: CORRADO MASSA Via Fratelli Manfredi 66 1-42100 Reggio Emilia, Italy </p><p>Annalen der Physik Verlag Johann Ambrosius Barth, SalomonstraDe 18 b, 0-i010 Leipzig, Ruf 70131 Chefredakteur: Prof. Dr. Dr. h.c. mult. H.-J. TBEDER, Rosa-Luxemburg-Str. 1 7 a, 0-1690 Potsdam-Babelsberg Veroffentlicht unter der Lizenznummer 1396 Satz, Druck und Einband: Druckhaus Kiithen GmbH, 0-4270 Kothen Printed in Germany AX (EDV) 51216 AN-ZV 111 8 000 436 Ymal jiihrlich Jahresbezugspreis 176, - DM Eincelheft 2,- DM </p></li></ul>