Quantization of Open strings in time dependent Black Holes

TL;DR

This paper quantizes open strings in a time-dependent black hole background, analyzing their two-point functions and incorporating finite temperature effects, revealing how string behavior adapts to dynamic spacetime geometries.

Contribution

It introduces a novel quantization of open strings in a time-dependent black hole background using an adiabatic approximation and explores finite temperature effects in this context.

Findings

Two-point functions exhibit flat space singularity types.

Equal time two-point functions depend on the chosen Cauchy surface.

Finite temperature effects are successfully incorporated.

Abstract

In this letter, the open string is quantized in a time dependent black hole background. The geometry is defined through an adiabatic approximation of the Vaydia metric. The worldsheet two-point function is derived and it is shown to have the same type of singularity as the flat space one. However, the equal times two-point function depends on the particular Cauchy surface where the worldsheet fields are defined. Finite temperature effects are incorporated through the Liouville-von Neumann approach to non equilibrium thermodynamics.