Fermion Tunneling Beyond Semiclassical Approximation

TL;DR

This paper extends the Hamilton-Jacobi tunneling method beyond the semiclassical approximation to analyze Hawking radiation of Dirac particles, revealing quantum corrections to temperature and entropy, and linking entropy corrections to trace anomaly.

Contribution

It introduces a method to incorporate quantum corrections in fermion tunneling, providing new insights into black hole thermodynamics beyond semiclassical results.

Findings

Quantum corrections to Hawking temperature are computed.

Logarithmic entropy correction coefficient is related to trace anomaly.

Modifications to Bekenstein-Hawking entropy are quantitatively analyzed.

Abstract

Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in \cite{Majhi3} for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.