Quantum Tunneling Beyond Semiclassical Approximation

TL;DR

This paper presents a Hamilton-Jacobi formalism to compute quantum corrections to Hawking radiation beyond the semiclassical approximation by including all higher-order terms in the single-particle action. The authors show that these corrections are proportional to the semiclassical contribution and demonstrate how a simple parameterization reproduces known one-loop back-reaction effects and trace anomaly results, leading to modified Hawking temperatures for Schwarzschild and AdS-Schwarzschild black holes. Using the first law of black hole mechanics, they derive corrected Bekenstein-Hawking entropy, revealing a universal leading logarithmic term in the entropy with subsequent inverse-area corrections. The framework is shown to be coordinate-independent and applicable to non-spherically symmetric spacetimes (e.g., Kerr), thereby providing a consistent, factor-two-ambiguity-free description of quantum corrections with clear thermodynamic implications and broad applicability.

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.