Abstract
There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking’s original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. We study instantons of a massless scalar field in Einstein gravity. We consider a complex-valued instanton that connects an initial pure black hole state to a black hole with a scalar field that represents the Hawking radiation at future null infinity, where its action depends only on the areal entropy difference. By comparing it with several independent approaches to Hawking radiation in the perturbative limit, we conclude that Hawking radiation may indeed be described by a family of instantons. Since the instanton approach can describe non-perturbative processes, we hope that our new interpretation and holistic method may shed lights on the information loss problem.
Highlights
One difficulty is that there exist only limited tools at hand to deal with the physics of black hole evaporation
We know that once gravity is taken into account, instantons can describe phenomena associated with vacuum fluctuations that are consistent with that deduced from the perturbative quantum field theory [25,26,27]
Our result reveals that instanton approach can recapitulate the Hawking radiation with a thermal spectrum
Summary
The scattering amplitude from an in-state (defined at the past null infinity, say (hainb, φin)) to an out-state (defined at the future null infinity, say (haoubt, φout)) (Fig. 1) is formally defined by the path-integral, h out ab. This integral is not easy to evaluate in practice, extrapolating the flat space quantum field theory, we may assume that it can be evaluated by the analytic continuation to the Euclidean time t = −iτ [41]:. We answer the first question and clarify that there exists a continuous family of non-trivial instanton solutions that are real at future null infinity.
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