Renormalized stress-energy tensor of an evaporating spinning black hole

TL;DR

This paper calculates the renormalized stress-energy tensor of a quantum scalar field around an evaporating spinning black hole using a new mode-sum regularization method, providing insights into semiclassical effects and black hole evaporation.

Contribution

It applies a recent mode-sum regularization technique to Kerr black holes, specifically for a massless scalar field in the Unruh vacuum, demonstrating consistent results with different splitting methods.

Findings

Good agreement between $t$-splitting and $$-splitting methods.

Results relevant for semiclassical corrections to black hole metrics.

Potential applications in simulating black hole evaporation.

Abstract

We employ a recently developed mode-sum regularization method to compute the renormalized stress-energy tensor of a quantum field in the Kerr background metric (describing a stationary spinning black hole). More specifically, we consider a minimally-coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case $a=0.7M$, using two different variants of the method: $t$-splitting and $\varphi$-splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.