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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
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The starting point
Big question:
How does the producedmatter thermalize so fast?
Perturbation theory +Kinetic equations
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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
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Black holes radiate
Hawking radiation
Black holes emitthermal radiationwith temperature
S.Hawking ‘74
acceleration of gravityat the surface
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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
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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
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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…
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well, now we need some quantum mechanics, too:
The rate of tunnelingunder the potential barrier:
This is a Boltzmann factor with
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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
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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:
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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!
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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!
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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
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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
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Fast thermalization
Rindler coordinates:
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collision pointQs
horizons
Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell in t=2Qs
(period of Euclidean motion)
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Rapid deceleration induces phase transitions
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Nambu-Jona-Lasinio model(BCS - type)
Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric
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Hawking radiation
New link between General Relativity and QCD;solution to some of the RHIC puzzles?
RHIC event