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 HRBH-Th BH-E BH-TeLHC QBH-E GR QM AO