# Semiclassical gravity effects near horizon formation

## TL;DR

This paper investigates semiclassical gravity effects near horizon formation in spherically symmetric spacetimes, analyzing quantum field effects during different matter surface movements and their impact on Hawking radiation and stress-energy tensor.

## Contribution

It provides a detailed analysis of quantum effects near horizon formation, including scenarios without horizon formation and deviations from classical evolution.

## Key findings

- Hawking-like radiation can occur without horizon formation.
- Large stress-energy tensor values are linked to Boulware vacuum divergence.
- Different surface dynamics lead to varied semiclassical effects.

## Abstract

We study the magnitude of semiclassical gravity effects near the formation of a black-hole horizon in spherically-symmetric spacetimes. As a probe for these effects we use a quantised massless scalar field. Specifically, we calculate two quantities derived from it: the renormalised stress-energy tensor (a measure of how the field vacuum state affects the spacetime) and the effective temperature function (a generalisation of Hawking temperature related to the energy flux of the field vacuum). The subject of our study are spacetimes which contain a spherical distribution of matter and an empty exterior Schwarzschild region, separated by a surface which is moving in proximity to the Schwarzschild radius $r_{\rm s}=2M$, with $M$ the total mass. In particular, we analyse the consequences of three types of surface movement: an oscillation just above $r_{\rm s}$, a monotonous approach towards $r_{\rm s}$ in infinite time and a crossing of $r_{\rm s}$ at different velocities. For a collapsing matter distribution which follows the expected dynamical evolution in general relativity, we recover the standard picture of black-hole formation and its tenuous semiclassical effects. In more general dynamical regimes, allowing deviations from the standard classical evolution, we obtain a variety of different effects: from the emission of Hawking-like radiation without the formation of a horizon, to large values of the renormalised stress-energy tensor, related to the Boulware vacuum divergence in static spacetimes.