Heavy Ions Collisions and Black Holes Production Irina

Heavy Ions Collisions and Black Holes Production Irina Aref’eva Steklov Mathematical Institute, Moscow Round Table IV Italy-Russia@ Dubna Black Holes in Mathematics and Physics December 16 -17, 2011

Outlook • Theoretical problems of BH formation: • • Semiclassical approach and geometrical cross section; Trapped surface arguments • Dual description of QCD: • • • QGP in dual description; Trapped surface area and multiplicity; BH charge and chemical potential

BH formation in collision of matter • 4 -dim (astrophysics) • Te. V Gravity (micro-black holes) D-dim, D= 5, 6, … • 5 -dim Ad. S to 4 -dim QCD

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

BLACK HOLE FORMATION 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

4 -dim • 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

D-dim, D= 5, 6, … • Te. V Gravity (1998) N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, I. Antoniadis, 1998 • Te. V 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• Classical geometric cross-section has got support from trapped surface estimations R. Penrose, unpublished, 1974 D. M. Eardley and S. B. Giddings, 2002 H. Yoshino and Y. Nambu, 2003 S. B. Giddings and V. S. Rychkov, 2004 ………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)

Metric of the space-time with shock wave • MD with a shock wave (Aichelburg-Sexl metric) M. Hotta, M. Tanaka – 1992

Eikonal approximation + …. Guidice, Rattazzi, Well, hep-ph/0112161, Lodone, Rychkov, 0909. 3519 Barbashov, Kuleshov, Matveev, Sissakian, TMP, 1970 Kadyshevskii at al, TMP, 1971

Geodesics in the space-time with shock wave U V X

2 Ultrarelativistic particles = 2 shock waves • 2 Aichelburg-Sexl shock waves Smooth coordinates: P. D’Eath coordinates, Dray and ‘t Hooft M. Hotta, M. Tanaka – 1992

Trapped Surface for two shock waves U V X TS comprises two halves, which are matched along a “curve” Eardley, Giddings; Kang, Nastase, ….

Trapped Surface for two shock waves The TS has two parts which lie in the regions They are defined in terms of two functions Boundary condition:

Black Hole production in Ad. S 5 as Quark-Gluon-Plasma formation in 4 -dim QCD Goal: construct colliding nuclei in a holographic dual to QCD (an exact holographic dual to QCD is unavailable) Gold ions colliding with √s. NN ~200 Ge. V produces entropy ~ 38 000: Conjecture: Total entropy production in a heavy-ion collision = entropy of a trapped surface. Nastase, hep-th/0501068; Shuryak, Sin, Zahed; Grumiller, Romatschke; Albacete, Kovchegov, Taliotis(09)

Shock-waves in Ad. S 5 z=0 & 4 -dim QCD Our 4 -dim world N=4 SYM 5 -dim SUGR in Ad. S space 5 th coord. z L is the radius of the Ad. S space L= -6/L 2

Single Nucleus in Ad. S/CFT An ultrarelativistic nucleus is a shock wave in 4 d with the energy-momentum tensor The metric of a shock wave in Ad. S corresponding to the ultrarelativistic nucleus in 4 d is Janik, Peschanksi ‘ 05

Colliding Nuclei in Ad. S/CFT Nothing happens before the collision

Multiplicity Gubser, Pufu, Yarom, 0805. 1551, Alvarez-Gaume, C. Gomez, Vera, Tavanfar, and Vazquez-Mozo, 0811. 3969 GQP = BH Lattice calculations

Different profiles and multiplicities An arbitrary gravitational shock wave in Ad. S 5 Plane shock waves Lin and Shuryak, 09 The Einstein equation Dilaton shock waves Cai, Ji, Soh, gr-qc/9801097 IA, 0912. 5481 Kiritis, Taliotis, 1111. 1931

“Trapped Surface” for two shock waves Regularization

Critical trapped surfaces formation in the collision of ultrarelativistic charges in (A)d. S A trapped surface forms if Formation of trapped surfaces on the past light cone is only possible when IA, A. Bagrov, E. Guseva, JHEP (2010) (d. S, Ad. S) IA, A. Bagrov, L. Joukovskaya, JHEP (2010) (charged particles in Ad. S, d. S)

Critical trapped surfaces formation in the collision of charged shock waves in (A)d. S The trapped surface decreases with growth of a charge.

Conclusion • BH production in Ad. S 5 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 Ad. S 5 with “stars”