Linear growth of the two-point function for the Unruh state in $1+1$ dimensional black holes

TL;DR

This paper investigates the linear growth of the two-point function for a massless scalar field in the Unruh state within 1+1 dimensional black hole spacetimes, revealing universal late-time behavior across various models.

Contribution

It demonstrates the linear growth of the two-point function in the Unruh state for 2D black holes and discusses its generalization to massive fields and different spacetimes.

Findings

Two-point function grows linearly with time in 2D black hole spacetimes.

Behavior is universal across static and collapsing black hole models.

Results extend to massive scalar fields in Schwarzschild-de Sitter spacetime.

Abstract

The symmetric two-point function for a massless, minimally coupled scalar field in the Unruh state is examined for Schwarzschild-de Sitter spacetime in two dimensions. This function grows linearly in terms of a time coordinate that is well-defined on the future black hole and cosmological horizons, when the points are split in the space direction. This type of behavior also occurs in two dimensions for other static black hole spacetimes when the field is in the Unruh state, and at late times it occurs in spacetimes where a black hole forms from the collapse of a null shell. The generalization to the case of the symmetric two-point function in two dimensions for a massive scalar field in Schwarzschild-de Sitter spacetime is discussed.