Hawking radiation as tunneling Baocheng Zhang Wuhan institute of Physics and Mathematics Chinese...
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Hawking radiation as tunneling
Baocheng Zhang
Wuhan institute of Physics and Mathematics Chinese Academy of Sciences
The coauthors:
Qing-yu Cai
Ming-sheng Zhan
Backgroud
Hawking radiation as tunneling through quantum horizon
Hawking radiation Bogoljubov transformation relating in-modes
which determine the state of the radiation field before the collapse and out-modes which define the particles emerging from the hole and found at infinity.
Treat the black hole immersed in a thermal bath
comment: in both of the standard calculations, the background geometry is considered fixed, and energy conservation is not enforced during the emission process.
Hawking radiation as tunneling The consideration: energy conservation The coordinate system: Painleve coordinate The particles: infinite blueshift near the horizon The barrier: the outgoing particle itself The method: The WKB approximation The physical picture: tunneling PRL 85, 5042 (2000)
The important result obtained in
such picture
Comment: This recover the Hawking radiation in leading
order
The physical picture
The relation between radiation and entropy
The non-thermal spectrum
The generalization
Black hole thermodynamics
Generalized Second Law
Black hole information loss paradox
Hawking’s proposal to accept the information loss
Black hole remnant——infinite degeneracy
Quantum hair——how to reduce to low energy
The information hidden in radiation——the quantity
The final state projection——whether it exist
Quantum black hole Motivation——Paradox
Counting microstates of black holes
Black hole complementarity
The holographic principle
The string theory and field theory
The ultraviolet-infrared connection
The quantum modification of entropy
The microstates counting
The one-loop effect of quantum matter fields near a black hole
Purely quantum gravity effect
Background
Hawking Radiation
Black hole thermodynamics
Quantum black hole
Review
Tunneling probability
Thermodynamics and tunneling
The entropy change method review
The metric:
The outgoing radial null geodesics near horizon
The surface gravity
The temperature of the radiation
PLB 660, 402 (2008)
The change of the entropy:
Thus we obtain the tunneling probability from the change of entropy as a direct consequence of the first law of black hole thermodynamics.
The problem The entropy modified by quantum gravity effect:
We calculate the change of the entropy
This is inconsistent with the result obtained by calculating the
imaginary part of the action included quantum gravity effect.
Why does it lead to such problem?
It looks as if formally the temperature were not proportional to the surface gravity according to the first law of black hole thermodynamics, when the entropy is modified by quantum gravity effect.
?
Solution We must hold the first law of black hole thermodynamics
and the temperature relation, so
The surface gravity defined afresh sustains the proportional relation between the temperature and surface gravity and the first law of black hole thermodynamics is held.
The tunneling probability through quantum horizon
Conclusion The tunneling probability can be obtained from the
first law of thermodynamics by using the method of the change of entropy with logarithmic correct which contains quantum gravity effect.
The proportional relation between the temperature and the surface gravity plays the important role.
The generalization verifies the connection of black hole radiation with thermodynamics further.
Baocheng Zhang, Qing-yu Cai and Ming-sheng Zhan, PLB 665, 260 (2008)
Future
Baocheng Zhang, Qing-yu Cai and Ming-sheng Zhan, “Entropy conservation in Hawking radiation as tunneling”, submitted for publication
BH-I-L-P
Unruh E
HR BH-Th
BH-E
BH-Te LHC
QBH-E
GR
QM
AO