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Heavy Ions Collisions and Black Holes Production Irina Aref’eva

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

  2. 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

  3. BH formation in collision of matter • 4-dim (astrophysics) • TeV Gravity (micro-black holes) D-dim, D= 5, 6,… • 5-dim AdS to 4-dim QCD

  4. BLACK HOLE FORMATION • Thorn's hoop conjecture: BH forms if the linear size of clumping matter l is comparable to the Schwarzschild radius Rsof 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 Rsof a BH of mass E. • Classicalgeometricalcross-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 Collidingplane 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 Classical geometric cross-section has got support from trapped surface estimations R.Penrose, unpublished, 1974 D.M.Eardley and S.B. Giddings, 2002 H.Yoshino and Y. Nambu, 2003 S. B. Giddings and V. S. Rychkov, 2004 ………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. Metric of the space-time with shock wave • MD with a shock wave (Aichelburg-Sexl metric) M. Hotta, M. Tanaka – 1992

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

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

  13. 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

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

  15. 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:

  16. Black Hole production in AdS5 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 √sNN ~200 GeV 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)

  17. Shock-waves in AdS5 & 4-dim QCD Our 4-dim world N=4 SYM z=0 5-dim SUGR in AdS space 5th coord. z L is the radius of the AdS space L= -6/L2

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

  21. Different profiles and multiplicities An arbitrary gravitational shock wave in AdS5 Plane shock waves Lin and Shuryak, 09 The Einstein equation Cai,Ji,Soh, gr-qc/9801097 Dilaton shock waves IA, 0912.5481 Kiritis,Taliotis, 1111.1931

  22. “Trapped Surface” for two shock waves Regularization

  23. Critical trapped surfaces formation in the collision of ultrarelativistic charges in (A)dS 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) (dS, AdS) IA, A.Bagrov, L.Joukovskaya, JHEP (2010) (charged particles in AdS,dS)

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

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