Versatile method for renormalized stress-energy computation in black-hole spacetimes

TL;DR

This paper introduces a versatile new method for calculating the renormalized stress-energy tensor in black-hole spacetimes, applicable to various black-hole types, and explores quantum effects like energy condition violations near black holes.

Contribution

The paper presents a novel, adaptable method for RSET computation in black-hole spacetimes with a single symmetry, extending to dynamical and spinning black holes.

Findings

RSET is type I at weak fields, type IV near the horizon.

Weak and null energy conditions are violated from approximately 4.9M to the horizon.

The averaged null energy condition is violated at the circular null geodesic at 3M.

Abstract

We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. So far we developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally-coupled massless scalar field in Schwarzschild and Reissner-Nordstrom backgrounds, for several quantum states. We present here the results for the RSET in the Schwarzschild case in Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at $r\lesssim2.78M$. Then we use the RSET results to explore violation of the weak and null Energy conditions. We find that both conditions are violated all the way from $r\simeq4.9M$ to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at $r=3M$ violates the averaged null energy condition.