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