Quantum Black Holes and Relativistic Heavy Ions

1. 21st Winter Workshop on Nuclear Dynamics, Breckenridge, February 5-11, 2005 Quantum Black HolesandRelativistic Heavy Ions D. Kharzeev BNL based on DK & K. Tuchin, hep-ph/0501234

2. The starting point Big question: How does the produced matter thermalize so fast? Perturbation theory + Kinetic equations

3. Outline • An elementary theory of the Hawking-Unruh radiation • A hidden path through the event horizon: from CGC to QGP in less than a fermi • Phase transitions • Possible solutions to some of the RHIC puzzles

4. Hawking radiation Black holes radiate S.Hawking ‘74 Black holes emit thermal radiation with temperature acceleration of gravity at the surface

5. Similar things happen in non-inertial frames Einstein’s Equivalence Principle: Gravity Acceleration in a non-inertial frame An observer moving with an acceleration a detects a thermal radiation with temperature W.Unruh ‘76

6. In both cases the radiation is due to the presence of event horizon Black hole: the interior is hidden from an outside observer; Schwarzschild metric Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric

7. Thermal radiation can be understood as a consequence of tunneling through the event horizon You don’t need to know anything except relativistic classical mechanics to understand this: velocity of a particle moving with an acceleration a classical action: it has an imaginary part…

8. well, now we need some quantum mechanics, too: The rate of tunneling under the potential barrier: This is a Boltzmann factor with

9. An example: electric field The force: The acceleration: The rate: What is this? Schwinger formula for the rate of pair production; an exact non-perturbative QED result factor of 2: contribution from the field

10. A quantum observer consider an observer with internal degrees of freedom; for energy levels E1 and E2 the ratio of occupancy factors J. Bell: depolarization in accelerators? For the excitations with transverse momentum pT:

11. but this is all purely academic (?) Take g = 9.8 cm/s2; the temperature is only Where on Earth can one achieve the largest acceleration (deceleration) ? Relativistic heavy ion collisions!

12. Why not hadron collisions? Consider a dissociation of a high energy hadron of mass m into a final hadronic state of mass M; The probability of transition: Transition amplitude: In dual resonance model: b=1/2 universal slope Unitarity:P(mM)=const, Hagedorn temperature! limiting acceleration

13. Color Glass Condensate as a necessary condition for the formation of Quark-Gluon Plasma The critical acceleration (or the Hagedorn temperature) can be exceeded only if the density of partonic states changes accordingly; this means that the average transverse momentum of partons should grow CGC QGP

14. Quantum thermal radiation at RHIC The event horizon emerges due to the fast decceleration of the colliding nuclei in strong color fields; Tunneling through the event horizon leads to the thermal spectrum Rindler and Minkowski spaces

15. Fast thermalization horizons Rindler coordinates: collision point Qs Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell int=2Qs (period of Euclidean motion)

16. Rapid deceleration induces phase transitions Nambu- Jona-Lasinio model (BCS - type) Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

17. Hawking radiation New link between General Relativity and QCD; solution to some of the RHIC puzzles? RHIC event