Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell

TL;DR

This paper presents a new method for calculating the stress-energy tensor of a quantized scalar field during black hole formation from null shell collapse, involving mode matching and renormalization techniques.

Contribution

It introduces a novel approach to compute the stress-energy tensor in dynamic black hole spacetimes, extending previous methods to a more general collapsing scenario.

Findings

Method successfully applied in 2D case with known results

Provides a systematic way to handle mode matching and renormalization

Lays groundwork for extending calculations to 4D black hole formation

Abstract

A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy tensor for the field in the Unruh state. The method is shown to work in the two-dimensional case where the results are known.