Renormalized stress tensor for massive fields in Kerr-Newman spacetime

TL;DR

This paper derives analytical approximations for the renormalized stress-energy tensor of massive quantum fields in Kerr-Newman spacetime, aiding the study of quantum effects on rotating charged black holes.

Contribution

It provides the first analytical expressions for the stress-energy tensor of various massive fields in Kerr-Newman spacetime, extending previous results from simpler black hole models.

Findings

Derived explicit formulas for scalar, Dirac, and Proca fields.

Reproduced known results for Schwarzschild, Reissner-Nordström, and Kerr black holes.

Facilitates analysis of quantum backreaction and quasinormal modes in Kerr-Newman spacetime.

Abstract

In a four-dimensional spacetime, the DeWitt-Schwinger expansion of the effective action associated with a massive quantum field reduces, after renormalization and in the large mass limit, to a single term constructed from the purely geometrical Gilkey-DeWitt coefficient $a_3$ and its metric variation provides a good analytical approximation for the renormalized stress-energy tensor of the quantum field. Here, from the general expression of this tensor, we obtain analytically the renormalized stress-energy tensors of the massive scalar field, the massive Dirac field and the Proca field in Kerr-Newman spacetime. It should be noted that, even if, at first sight, the expressions obtained are complicated, their structure is in fact rather simple, involving naturally spacetime coordinates as well as the mass $M$, the charge $Q$ and the rotation parameter $a$ of the Kerr-Newman black hole and permitting us to recover rapidly the results already existing in the literature for the Schwarzschild, Reissner-Nordstr\"om and Kerr black holes (and to correct them in the latter case). In the absence of exact results in Kerr-Newman spacetime, our approximate renormalized stress-energy tensors could be very helpful, in particular to study the backreaction of massive quantum fields on this spacetime or on its quasinormal modes.