On 4D-Hawing Radiation from Effective Action

TL;DR

This paper calculates the s-wave contribution of a scalar field to the 4D effective action in spherically symmetric gravitational fields, demonstrating that the resulting energy-momentum tensor includes Hawking radiation and can inform backreaction studies.

Contribution

It provides a method to derive the energy-momentum tensor from the effective action that captures Hawking radiation in 4D black holes.

Findings

Energy-momentum tensor contains Hawking radiation.

Luminosity close to expected s-channel value.

Method applicable to backreaction analysis.

Abstract

We determine the $s$-waves contribution of a scalar field to the four dimensional effective action for arbitrary spherically symmetric external gravitational fields. The result is applied to $4d$-black holes and it is shown that the energy momentum tensor derived from the (nonlocal) effective action contains the Hawking radiation. The luminosity is close to the expected one in the $s$-channel. The energy momentum tensor may be used as starting point to study the backreaction problem.