On Hawking Radiation as Tunneling with Logarithmic Corrections

TL;DR

This paper investigates whether the tunneling approach to Hawking radiation, including quantum logarithmic corrections to entropy, can resolve the black hole information paradox, concluding it cannot and constraining the correction coefficient.

Contribution

It demonstrates that the tunneling formalism cannot resolve the information paradox even with logarithmic quantum corrections and constrains the correction coefficient to be non-negative.

Findings

Tunneling formalism does not resolve the information paradox with quantum corrections.

Logarithmic correction coefficient must be non-negative.

Canonical corrections are necessary in quantum black hole entropy formulation.

Abstract

There has been recent speculation that the tunneling paradigm for Hawking radiation could -- after quantum-gravitational effects have suitably been incorporated -- provide a means for resolving the (black hole) information loss paradox. A prospective quantum-gravitational effect is the logarithmic-order correction to the Bekenstein-Hawking entropy/area law. In this letter, it is demonstrated that, even with the inclusion of the logarithmic correction (or, indeed, the quantum correction up to any perturbative order), the tunneling formalism is still unable to resolve the stated paradox. Moreover, we go on to show that the tunneling framework effectively constrains the coefficient of this logarithmic term to be non-negative. Significantly, the latter observation implies the necessity for including the canonical corrections in the quantum formulation of the black hole entropy.