Heavy Ions Collisions

andBlack Holes Production

Irina Aref’eva

Steklov Mathematical Institute, Moscow

Round Table IV Italy-Russia@ DubnaBlack Holes in Mathematics and Physics

December 16-17, 2011

Outlook

• Dual description of QCD:• QGP in dual description;• Trapped surface area and multiplicity;• BH charge and chemical potential

• Theoretical problems of BH formation:• Semiclassical approach and geometrical cross section;• Trapped surface arguments

• 4-dim (astrophysics)

• TeV Gravity (micro-black holes)

D-dim, D= 5, 6,…

• 5-dim AdS to 4-dim QCD

BH formation in collision of matter

BLACK HOLE FORMATION

• Thorn's hoop conjecture:

BH forms if the linear size of clumping matter l is

comparable to the Schwarzschild radius

Rs of a BH of mass m

Sl R 2SR Gm

BLACK HOLE FORMATION

2 2 2S(1 1 BH ) ~ ~ E R G

Modified Thorn's hoop conjecture (for colliding particles):

BH forms if the impact parameter b is comparable to the Schwarzschild radius Rs of a BH of mass E.

• Classical geometrical cross-section

• In 1987 't Hooft and Amati, Ciafaloni and Veneziano conjectured that in string theory and in QG at energies much higher than the Planck mass BH emerges.

Aichelburg-Sexl shock waves to describe particles,

Shock Waves ------ > BH

• Colliding plane gravitation waves to describe particles

Plane Gravitational Waves ----- > BH I.A., Viswanathan, I.Volovich, Nucl.Phys., 1995

• Boson stars (solitons) to describe particles M.Choptuik and F.Pretorius, Phys.Rev.Lett, 2010

4-dim Gev19Pl 10 M

D-dim, D= 5, 6,…

• TeV Gravity (1998) N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, I. Antoniadis, 1998

• TeV Gravity to produce BH at Labs (1999) Banks, Fischler, hep-th/9906038 I.A., hep-th/9910269, Giuduce, Rattazzi, Wells, hep-ph/0112161 Giddings, hep-ph/0106219 Dimopolos, Landsberg, hep-ph/0106295, ……………………………

• Classical geometric cross-section has got support from trapped surface estimations

R.Penrose, unpublished, 1974D.M.Eardley and S.B. Giddings, 2002H.Yoshino and Y. Nambu, 2003S. B. Giddings and V. S. Rychkov, 2004

………

Trapped Surface

• A trapped surface is a two dimensional spacelike surface whose two null normals have negative expansion (=Neighbouring light rays, normal to the surface, must move towards one another)

• MD with a shock wave (Aichelburg-Sexl metric)

Metric of the space-time with shock wave

M. Hotta, M. Tanaka – 1992

2 2 24

( ) ( ) , ( )i i iD

cds dudv dx F x u du F x

+ ….

Guidice, Rattazzi,Well, hep-ph/0112161,Lodone, Rychkov,0909.3519

Barbashov,Kuleshov, Matveev,Sissakian, TMP,1970

Kadyshevskii at al, TMP,1971

Eikonal approximation

X

Geodesics in the space-time with shock wave

2

( ) ( )

( ) ( ) 2 ( ) ( )

X b v

V v F b

)(bFv

V

U

• 2 Aichelburg-Sexl shock waves

2 Ultrarelativistic particles = 2 shock waves

M. Hotta, M. Tanaka – 1992

4

2 2 2 21 2

2 20

( )( ) ( ) ( ) ( ) ,

( )

| ( ) |D

i i i i

i kk

i ik

ds dudv dx F x x u du F x v dv

cF x

x x

Smooth coordinates: P.D’Eath coordinates, Dray and ‘t Hooft

VU

X

Trapped Surface for two shock waves

,][ )2()2()1()1(2 jiijjkikjkik dXdXHHHHdUdVds

1,2 1,2

2 ( 2)1,2 (1,2)

1 2

0, , 0,

( ), ,

4,

D

the outer null normals have zero

convergenc

X D X D

X X

e

no function in convergence

X D

X D

Eardley, Giddings; Kang, Nastase,….

(1)1

1( )

2ij ij i jH F u u

TS comprises two halves,which are matched along a “curve”

The TS has two parts which lie in the regions

They are defined in terms of two functions

0Wand0

Boundary condition:

Trapped Surface for two shock waves

Black Hole production in AdS5 as Quark-Gluon-Plasma formation in 4-dim QCD

Conjecture: Total entropy production in a heavy-ion collision = entropy of a trapped surface.

Goal: construct colliding nuclei in a holographic dual to QCD (an exact holographic dual to QCD is unavailable)

Nastase, hep-th/0501068; Shuryak, Sin, Zahed; Grumiller, Romatschke; Albacete, Kovchegov,Taliotis(09)

Gold ions colliding with √sNN ~200 GeV produces entropy ~ 38 000:

z=0Our 4-dim worldN=4 SYM

5-dim SUGR in AdS space

L is the radius of the AdS space= -6/L2

5th coord. z 22

2

22 2 dzdxdxdx

z

Lds

2

30 xxx

Shock-waves in AdS5 & 4-dim QCD

Single Nucleus in AdS/CFT

An ultrarelativistic nucleus is a shock wave in 4d with the energy-momentum tensor

)(~ xT

The metric of a shock wave in AdS corresponding to the ultrarelativistic nucleus in 4d is

22242

2

2

22 )(

22 dzdxdxzxT

Ndxdx

z

Lds

C

Janik, Peschanksi ‘05

x

x

Colliding Nuclei in AdS/CFT

x

x

24

22

224

12

222

2

22 )(

2)(

22 dxzxT

NdxzxT

Ndzdxdxdx

z

Lds

CC

Nothing happens before the collision

Multiplicity

GQP = BH

Lattice calculations

Gubser, Pufu, Yarom, 0805.1551, Alvarez-Gaume, C. Gomez, Vera, Tavanfar, and Vazquez-Mozo, 0811.3969

Different profiles and multiplicities

An arbitrary gravitational shock wave in AdS5

Lin and Shuryak, 09

The Einstein equation

Plane shock waves

Cai,Ji,Soh, gr-qc/9801097

IA, 0912.5481

Kiritis,Taliotis, 1111.1931

Dilaton shock waves

“Trapped Surface” for two shock waves

Regularization

Critical trapped surfaces formation in the collision of ultrarelativistic charges in (A)dS

IA, A.Bagrov, E. Guseva, JHEP (2010) (dS, AdS)

IA, A.Bagrov, L.Joukovskaya, JHEP (2010) (charged particles in AdS,dS)

Formation of trapped surfaces on the past light cone is only possible when

crQ Q

A trapped surface forms if

The trapped surface decreases with growth of a charge.

Critical trapped surfaces formation in the collision of charged shock waves in (A)dS

Conclusion• BH production in AdS5 as QGP formation in 4-dim QCD• Techniques of trapped surfaces

Plans

• Classification of shock waves (to get details formula for multiplicity for heavy-ion collisions at RHIC and LHC)

• Try to use plane gravitational waves to calculate multiplicity• Simplification of techniques of trapped surface

• May be numerical calculations in AdS5 with “stars”