Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit

TL;DR

This paper investigates how classical soft graviton theorems are modified in an AdS-Schwarzschild background with a small cosmological constant, revealing corrections to flat space results.

Contribution

It introduces a perturbative analysis of soft graviton scattering in AdS-Schwarzschild spacetime and derives the correction to the classical soft theorem due to the AdS background.

Findings

Derived the correction to the flat space soft graviton theorem in AdS-Schwarzschild background.

Defined a proper soft limit in AdS spacetime for scattering processes.

Perturbative analysis consistent to leading order in AdS radius and black hole mass.

Abstract

We have studied scattering of a probe particle by a four dimensional AdS-Schwarzschild black hole at large impact factor. Our analysis is consistent perturbatively to leading order in the AdS radius and black hole mass parameter. Next we define a proper "soft limit" of the radiation and extract out the "soft factor" from it. We find the correction to the well known flat space Classical Soft graviton theorem due to the presence of an AdS background.