Hawking Radiation due to Photon and Gravitino Tunneling

TL;DR

This paper investigates photon and gravitino tunneling from black holes using the Hamilton-Jacobi method, deriving quantum corrections to Hawking temperature and entropy, and proposing a modified black hole metric incorporating these effects.

Contribution

It provides a detailed analysis of quantum corrections to Hawking radiation for photons and gravitinos, including gauge conditions and modified black hole metrics.

Findings

Quantum corrections proportional to semiclassical action.

Modified Hawking temperature and area law derived.

Corrected black hole metric consistent with one-loop back reaction.

Abstract

Applying the Hamilton--Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking's periodicity argument, the modified metric for the Schwarzschild black hole is given. This corrected version of the metric, upto $\hbar$ order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.