Gravitational wave memory for a class of static and spherically symmetric spacetimes

TL;DR

This paper compares gravitational wave memory effects across different static, spherically symmetric spacetimes to identify unique signatures that distinguish various compact objects based on geodesic evolution.

Contribution

It proposes a method to differentiate compact object geometries by analyzing displacement and velocity memory effects in various static, spherically symmetric spacetimes.

Findings

Memory effects vary distinctly between different spacetime geometries.

Permanent geodesic deviations serve as signatures of specific compact objects.

The approach enables differentiation of compact objects based on gravitational wave memory.

Abstract

This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating between various compact object geometries. We do this by considering the relative evolution of two nearby test geodesics with in different backgrounds in the presence and absence of a gravitational wave pulse and comparing them. Memory effect due to a gravitational wave would ensure that there is a permanent effect on each spacetime and the corresponding geodesic evolution, being metric dependent, would display distinct results in each case. For a complete picture, we have considered both displacement and velocity memory effect in each geometry.