Mini Black Holes - pds4.egloos.compds4.egloos.com/pds/200706/10/64/apctp_pohang_20070610.pdf · Rotating Black Holes at future colliders I: ... SPARK, Phys.Rev.D71:124039,2005. III:

Seong Chan Park

SNURotating Black Holes at future colliders

I: Greybody factors for brane fieldsD. Ida, K.-y. Oda, SPARK, Phys.Rev.D67:064025,2003, Erratum-ibid.D69:049901,2004.

II: Anisotropic scalar field emissionD. Ida, K.-y. Oda, SPARK, Phys.Rev.D71:124039,2005.

III: Determination of black hole evolutionD. Ida, K.-y. Oda, SPARK, Phys.Rev.D73:124022,2006.

Suppose that you want to make a black hole for your wife.. How can you make it?

Hoop Conjecture (Kip Thorne 1972) states

An imploding object forms a Black Hole when, and only when, a

circular hoop with a specific critical circumference could be placed around the object and rotated. The critical circumference is given by 2 times Pi times the Schwarzschild Radius corresponding to the objects mass.

So, build enough energy in a small space !!

Mini-BH, APCTP, Pohang 2007 June 10

Its like putting an elephant into a freezer..


Particle Physicists idea Collide two particles with a big CM energy.


( ,0,0, )E E

( ,0,0, )E E

62 10CM PlE E M

62 2 10 /S CM PlR GE M

b

If the impact parameter is smaller than Million times Planck length, a black hole forms.

2( 1/ )PlG M

G. 't Hooft Phys.Lett.B198, 61 (1987)

60.5 10 PlE M

Current technology (and budget) allows us just limited amount of CM energy.

LEP-II (CERN) : 200 GeV (closed)

Tevatron (Fermi Lab.) : 2 GeV (running)

The LHC (CERN): 14 TeV(from 2008-)


1 12 CM

Pl Pl Pl

Eb

M M M

Require enormous adjustment:

19

1TeV=1000 GeV

1.21 10 GeVPlM

It seems impossible to make a BH.

Wait! If there are extra dimensions, gravity becomes

stronger at small distances:

Also notice that the Planck scale has to be renormalized:


4 2

4 2

, ( )

, ( )

C

n Cn

MmG r r

r

MmG r r

r

4 4

" ( )" 1

n

Vol n

G G 2 2

4 4" ( )"n

nM Vol n M

Current experimental data suggest Microscopic torsion-pendulum Experiment

TeV scale gravity is an open possibility.


197 mCr Hoyle et.al. Phys.Rev.D70:042004,2004

4 (1)TeVnM O

TeV gravity Is Realized in many string theory models.

Arkani-Hamed, Dimopoulos, Dvali, Phys.Lett.B429:263-272,1998.

L. Randall, R. Sundrum, Phys.Rev.Lett.83:3370-3373,1999

Is able to address Hierarchy problem.

( = why is Higgs so light?

= why gravity is so week? )

Got a lot of attention from physics community. (String theory community, GR community, Particle physics community, SF community )


Black hole by high energy collision The LHC as a black hole factory

T. Banks /W. Fischler, ``A model for high energy scattering in quantum gravity,''

hep-th/9906038.

S. B. Giddings / S. D. Thomas, ``High energy colliders as black hole factories: The end of short distance physics,''

Phys. Rev. D65, 056010 (2002)

S. Dimopoulos / G. L. Landsberg, ``Black holes at the LHC,''

Phys. Rev. Lett.87, 161602 (2001)

Black holes from the skyJ. L. Feng / A. D. Shapere, ``Black hole production by cosmic rays,''

PRL88, 021303 (2002)

L. Anchordoqui / H. Goldberg, ``Experimental signature for black hole production in neutrino air showers,''

PRD 65, 047502 (2002)

R. Emparan/ M. Masip /R. Rattazzi, ``Cosmic rays as probes of large extra dimensions and TeV gravity,''

PRD65, 064023 (2002)


Now we have obvious and urgent questions

Q1) How many black holes will be produced?

Determination of production cross section.

Q2)What will be their signals?

Determination of black holes life.

Decay pattern of black hole.

Need to calculate Greybody factors.


Set-up(1) Our black hole is best described by (4+n)Dimensional,

rotating black hole solution.R. C. Myers and M. J. Perry, ``Black Holes In Higher Dimensional Space-Times,''

Annals Phys. 172, 304 (1986).


222)4(2 cos),( ndrrgds

g(4)(r,)

a2 sin2

(r2 a2 )asin2

0 0

*[(r2 a2)2 a2 sin2 ]sin2

0 0

0 0

0

0 0 0

2 2

22

1 2

cos

1n

r a

ar

r r

Set-up(2) We live on 3-brane world. (as was suggested by ADD,

RS)


e

Electron, photon, gluon, quarks, Me, Don. N. Page, everything except graviton is confined on this hyper surface (D3).

iy

x

Bulk vs Brane emission Boltzmann law

d.o.f. (brane)=all the SM particles d.o.f.(bulk) = graviton

R. Emparan, G. T. Horowitz and R. C. Myers, ``Black holes radiate mainly on the brane,''

Phys. Rev. Lett.85, 499 (2000)


4 2 4

4 2

4 2 4

4 2

1 1/ ( ) ,(brane)

1 1/ ( ) ,(bulk)

( ) ( ), (for each d.o.f)

s

s s

n n n

n s

s s

dE dt A T rr r

dE dt A T rr r

dE dEbrane bulk

dt dt

Production Cross section


b

21

22

2max

2

214 S

n

rn

b

, / 2M J Mb

M/2

M/2

2 1/ 1

1/ 1

4

( , ) ( )(1 )

( ) ( ) , (1)

n

H S

n

S n n n

r M J r M a

r M C G M C O

22 1

21 ( ) 0ns

r ar

r r

Hoop Conjecture:

D. Ida, K.-y. Oda, S.PARK, Phys.Rev.D67:064025,2003, Erratum-ibid.D69:049901,

2004

Related numerical studies


cf) Numerical result utilizes

the Aichelburg-Sexl solution

Setup: two particles (BHs) with

boost,

mass0,

energy: fixed.

t

z

b

Closed trapped surface forms

when b < bmax.

D. M. Eardley and S. B. Giddings, ``Classical black hole production in high-energy collisions,''

Phys. Rev. D66, 044011 (2002)H. Yoshino and Y. Nambu,

``Black hole formation in the grazing collision of high-energy particles,'' Phys. Rev.D 67, 024009 (2003)

H. Yoshino, A. Zelnikov and V. P. Frolov, ``Apparent horizon formation in the head-on collision of gyratons,'' arXiv:gr-qc/0703127.

n 1 2 3 4 5 6 7

R Y N 1.056 1.158 1.228 1.276 1.314 1.344 1.368

R IO P 1.110 1.170 1.218 1.262 1.300 1.334 1.364

Sr

bnR max)(

Yoshino-Nambu (02), Yoshino et.al.(04,05)

Ida, Oda, Park PRD03

Error ~ a few %

Excellent Agreements in the Results:


BH Differential production cross section

2Sr

F

n 1 2 3 4 5 6 7

F Y N 1.084 1.341 1.515 1.642 1.741 1.819 1.883

F IO P 1.231 1.368 1.486 1.592 1.690 1.780 1.863

Geometrical Cross section

Form factor

)2/( maxmax MbJ

)(0

)(/8

max

max2

JJ

JJMJ

dJ

d

bdbd 2

db

Most of BHs are produced with

large angular momentum!

21

22

2max

2

214 S

n

rn

b


Decay of Black Hole Most of black holes are produced with large angular momentum.

Geometry is not spherically symmetric.

Hawking radiation is anisotropic, not equally probable.


medg

J

M

dt

dTm

mls

mlss

12

1/

,,

,,

:The probability is not equal to every particlebut crucially depends on spin and angular mode .

Anisotropic and nontrivial Hawking radiation is expected.

We have to know this greybody factor to understand HawkingRadiation.

, .s l m

A Good NewsRotating Black Holes at future colliders

I: Greybody factors for brane fieldsD. Ida, K.-y. Oda, SPARK, Phys.Rev.D67:064025,2003, Erratum-ibid.

D69:049901,2004.

II: Anisotropic scalar field emissionD. Ida, K.-y. Oda, SPARK, Phys.Rev.D71:124039,2005.

III: Determination of black hole evolutionD. Ida, K.-y. Oda, SPARK, Phys.Rev.D73:124022,2006.

Greybody factors for all the SM particles (s=0,1/2,1) are obtained in general (4+n)dimensional cases.


In this series of papers We developed analytic and numerical method to

understand Mini Black holes.

Cross section for BH production is estimated.

Hawking radiation in (4+n)D is fully calculated after taking greybody factors precisely.

Mini BHs Life is (almost) completely described.


Greybody factor

= Absorption Probability of wave mode (s, l, m) by BH.

= Modification factor to take the curved geometry NH

into account.

medg

J

M

dt

dTm

mls

mlss

12

1/

,,

,,

T

Looks not black to me.

It looks Grey!


Caution:

Our calculation is valid only if

Classical

Higher Dimensional

Trans-Planckian Domain.

1/ BH H CM r r

Large (or Warped) extra dimensions: Compactification radius is BIG

1/ 11 ( ) nBH BHBH

r GMM

2(1/ )nBH PlM G M or

NOTE) if Mp~ 1 TeV, E=14 TeV at the LHC, these relations are fine.


Teukolsky equation (Kerr)

=Wave equation for general (s,l,m) wave for 4D Kerr BH (1972,1973)

Solution to Teukolsky equation/ Greybody Factors

: Analytic and Numerical methods was developed by

Teukolsky-Press, Starobinsky, Unruh, Page in 1973-1976.

Hawking radiation and its evolution

: Hawking 1975, Page 1976 (4D)

Generalized to (4+n) for brane fields. Ida, Oda, Park-1 (PRD 04)

Analytic (5D),low energy: Ida,Oda,Park-1

Numerical ((4+n)D) :

s=0 Ida, Oda, Park-II (PRD 05),

Harris, Kanti (PLB 06), Duffy, Harris, Kanti, Winstanley (JHEP 05)

s=1/2,1 Ida, Oda, Park-III (PRD 06)

Casals,Kanti,Winstanley (for s=1 only) (JHEP 06)

Ida, Oda, Park-III (PRD 06)((4+n)D) including all the SM fields.

Brief History of Greybody Factor

for Rotating BHs.


Newman-Penrose FormalismNull Tetrad

Get equations for scalar, Weyl Spinor and Vector(2nd Rank symmetric spinor)on the background geometry of Myers-Perry by perturbation.


Generalized Teukolsky equation Turned out to be separable.(Petrov type-D)


0)1()csccot()cos( sinsin

1 22

aSAssmsas

d

dS

d

d

0)(224 2,,

2

1

RAamaK

irisK

dr

dR

dr

d

rr

r

ss

maarK

r

a

rr

ar

n

)(

1

cos

22

2

2

1

2

22

Spin-weighted-spheroidal harmonics

We have to solve this radial equation.

Analytic method Low energy approximation (D=5)


NH limit: FF limit:

Overlapping region

Matching here!

Greybody factors: D=5 Low energy approximation.


Cf) For s=0, V. P. Frolov and D. Stojkovic, Phys. Rev. D67, 084004 (2003)

D. Ida, K.-y. Oda, SPARK, Phys.Rev.D67:064025,2003, Erratum-ibid.D69:049901,2004.

Numerical method


1.Near Horizon FF

BC: Imposing Purely Incoming

2. Numerical IntegrationOf Teukolsky equation.

3. Read out

Ingoing& outgoing wave

D=4+n, D. Ida, K.-y. Oda, SPARK,

Phys.Rev.D71:124039,2005.

Phys.Rev.D73:124022,2006

D=4, D. N. Page, ``Particle Emission Rates From A Black Hole. 2

:Massless Particles From A Rotating Hole,'' Phys. Rev. D14, 3260 (1976).

Two main difficulties:

1. Imposing purely incoming BC at NH

r rH

1

Outgoing wave contamination is growing faster than the value we want to calculate!

incoming

R

:Error/value grows fast.

Outgoing


Idea:

Get rid of this part!

1

Now, we dont worry aboutthe outgoing wave contamination.Numerical integration is donefor

:Error/value decreases.


2. Separation of Ingoing and Outgoing parts at FF

s=0: (In) ~ (Out) s=1/2: (In) > (Out)s=1: (In) >> (Out)

Numerically difficult to separate since there is a big hierarchy!


Idea: Analytically expand the solution

We can always find the same order terms. By comparing them, we can safely separate In and Out parts.


Higgs-I : S-wave, Various Dimensions

D=4 D=6D=10D=8

l=m=0, a=0

After angle integration

and scaling w^{-2}

Area of Black hole event horizonMini-BH, APCTP, Pohang 2007 June 10

Ida, Oda, Park PRD 05

Higgs-II : S-wave (l=0), Rotating hole (a=0, .3,.6,.9)

D=10, l=m=0

D=5, l=m=0

a=0

a=.9

D=4, l=m=0

NOTE: low energy enhancement

appears in S-wave mode when

BH Is highly rotating.

.6

.3





S = 1=2; D = 5



D = 10; s = 1=2




Super-radiance modes: negative probability modes


Ida, Oda, Park PRD 06 Ida, Oda, Park PRD 06

D = 5; s = 1



D = 11; s = 1



Mini-BH, APCTP, Pohang 2007 June 10J

0 0.5 1 1.5 2 2.5

0

0.2

0.4

0.6

0.8

1

Mass vs Angular momentum

s

10d

SM

v

f

0 0.5 1 1.5 2 2.5

0

0.2

0.4

0.6

0.8

1

Angular momentum vs t/t(.01)

s

f

v

Time

10d

MJ Ida, Oda, Park PRD 06


0 0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

1

time

s

f

v

SM

5d

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

J

JM

5D

Time Evolution of Mini Black Hole (5D, 10D)

Black Holes Life

?

Time

Balding Phase

Spin Down Phase

Schwarzschild Phase

Planck Phase

(Production of BHs)

(Losing energy and angular momentum)

(Losing Mass)

(Remnant ???)

Todays topic.


Summary BH production cross section is estimated using Hoop

conjecture and taking angular momentum into account.

Greybody factors of D=4+n, rotating black holes are calculated for all the SM particles. (s=0,1/2,1)

BH decay by Hawking radiation is understood in the spin-down and Schwarzschild phases.


Open questions Still bulk gravitational radiation is missing.

(For non-rotating black hole)

A. S. Cornell, W. Naylor and M. Sasaki,

``Graviton emission from a higher-dimensional black hole,'' JHEP0602, 012 (2006)

Numerical simulation of scattering process

(Q. Can we use the BH-BH merging code?)

Table for Black hole hunters.M. Cavaglia, R. Godang, L. Cremaldi and D. Summers,

``Catfish: A Monte Carlo simulator for black holes at the LHC,'' arXiv:hep-ph/0609001.

Planck Phase. String theory? Quantum Information? Boltzmann-Brain???


Documents

Mini Black Holes - pds4.egloos.compds4.egloos.com/pds/200706/10/64/apctp_pohang_20070610.pdf · Rotating Black Holes at future colliders I: ... SPARK, Phys.Rev.D71:124039,2005. III: