1. 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

2. 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

3. 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

4. BLACK HOLE FORMATION Thorn's hoop conjecture : BH forms if the linear size of clumping matter l is comparable to the Schwarzschild radius R s of a BH of mass m

5. BLACK HOLE FORMATION Modified Thorn's hoop conjecture (for colliding particles) : BH forms if the impact parameter b is comparable to the Schwarzschild radius R s of a BH of mass E. Classical geometrical cross-section

6. 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

7. 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, ……………………………

8. Classical geometric cross-section has got support from trapped surface estimations R.Penrose, unpublished, 1974 D.M.Eardley and S.B. Giddings, 2002 H.Yoshino and Y. Nambu, 2003 S. B. Giddings and V. S. Rychkov, 2004 ………

9. 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 )

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

11. + …. Guidice, Rattazzi,Well, hep-ph/0112161, Lodone, Rychkov, 0909.3519 Barbashov, Kuleshov, Matveev, Sissakian, TMP,1970 Kadyshevskii at al, TMP,1971 Eikonal approximation

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

13. 2 Aichelburg-Sexl shock waves 2 Ultrarelativistic particles = 2 shock waves M. Hotta, M. Tanaka – 1992 Smooth coordinates: P.D’Eath coordinates, Dray and ‘t Hooft

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

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

16. Black Hole production in AdS 5 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 √s NN ~200 GeV produces entropy ~ 38 000:

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

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

19. Colliding Nuclei in AdS/CFT Nothing happens before the collision

20. Multiplicity GQP =BH Lattice calculations Gubser, Pufu, Yarom, 0805.1551, Alvarez-Gaume, C. Gomez, Vera, Tavanfar, and Vazquez-Mozo, 0811.3969

21. Different profiles and multiplicities An arbitrary gravitational shock wave in AdS 5 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

22. “Trapped Surface” for two shock waves Regularization

23. 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 A trapped surface forms if

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

25. 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 ”