Quantum Black Holesand

Relativistic Heavy Ions

D. Kharzeev

BNL

21st Winter Workshop on Nuclear Dynamics, Breckenridge, February 5-11, 2005

based onDK & K. Tuchin, hep-ph/0501234

The starting point

Big question:

How does the producedmatter thermalize so fast?

Perturbation theory +Kinetic equations

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

Black holes radiate

Hawking radiation

Black holes emitthermal radiationwith temperature

S.Hawking ‘74

acceleration of gravityat the surface

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 detectsa thermal radiation with temperature

W.Unruh ‘76

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

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…

well, now we need some quantum mechanics, too:

The rate of tunnelingunder the potential barrier:

This is a Boltzmann factor with

An example: electric fieldThe 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

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 inaccelerators?

For the excitations with transverse momentum pT:

but this is all purely academic (?)Take g = 9.8 cm/s2; the temperature is only

Where on Earth can one achieve the largestacceleration (deceleration) ?

Relativistic heavy ion collisions!

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:

Unitarity: P(mM)=const, b=1/2universal slope

limiting acceleration

Hagedorntemperature!

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 stateschanges accordingly;this means that the average transverse momentum of partons should grow

CGC QGP

Quantum thermal radiation at RHIC

The event horizon emerges due to the fastdecceleration of the colliding nucleiin strong color fields;

Tunneling throughthe event horizon leads to the thermalspectrum

Rindler and Minkowski spaces

Fast thermalization

Rindler coordinates:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

collision pointQs

horizons

Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell in t=2Qs

(period of Euclidean motion)

Rapid deceleration induces phase transitions

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Nambu-Jona-Lasinio model(BCS - type)

Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

Hawking radiation

New link between General Relativity and QCD;solution to some of the RHIC puzzles?

RHIC event