Quantum Tunneling Beyond Semiclassical Approximation

TL;DR

This paper investigates quantum corrections to Hawking radiation using the Hamilton-Jacobi tunneling method beyond semiclassical approximation, revealing modifications to black hole temperature and entropy consistent with conformal field theory results.

Contribution

It introduces a systematic way to compute quantum corrections to Hawking radiation beyond semiclassical approximation, linking them to back reaction effects and black hole thermodynamics.

Findings

Quantum corrections are proportional to semiclassical action.

Modified Hawking temperature matches conformal field theory predictions.

Corrections to Bekenstein-Hawking entropy are derived explicitly.

Abstract

Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.