Abstract
Abstract We investigated black hole evolution on a quantum-gravitational scattering framework with the aim of tackling the black hole information paradox. With this setup, various pieces of system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into a perturbative part and a non-perturbative part. The non-perturbative part is dominated by an instanton-type contribution, i.e. a black hole analogue of the Coleman–De Luccia bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vacuum expectation value of the Wald entropy charge. With this definition, a shifted Page-like curve is generically generated and its quantum extension is readily defined.
Highlights
Lack of quantizing gravity in a renormalizable manner has long been an obstacle to progress that would have otherwise been possible
One must consider -corrections to the bounce solution itself.) To capture such physics it will be crucial to start with a more realistic solution that we describe in the subsection
Black hole perturbation theory was developed long ago. (See, e.g., [20, 22] for reviews.) The classical quasi-normal mode (QNM) analysis reveals that a black hole radiates away most of its multipole characteristics, except the ones associated with mass, charge, and angular momentum
Summary
Lack of quantizing gravity in a renormalizable manner has long been an obstacle to progress that would have otherwise been possible. One thing worth noting is that in the present description of the Hawking radiation it is not necessary to construct a bulk solution that explicitly realizes a shrinking and evaporating black hole This part of the physics is accounted for by the bounce wormhole solution as a non-perturbative contribution to the path integral. (See the related comments in section 3.3.) it is the white whole state that accounts for the evaporated state: when the black hole evaporates, the mass is not lost, in the case of a Dirichlet boundary condition - but converted into the energy of the white hole state In other words, it is the novelty of vacuum decay physics that allows one to bypass explicit construction of a shrinking bulk solution. Appendix A contains some details regarding the bounce solution (6) in section 3 and its generalization
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