Displacement memory in regular black hole spacetimes

TL;DR

This study investigates displacement memory effects caused by gravitational wave pulses in regular black hole spacetimes, revealing parameter-dependent variations and differences from singular black holes through numerical analysis.

Contribution

It introduces a numerical analysis of displacement memory effects in regular black hole spacetimes using geodesic separation and deviation, highlighting parameter-dependent differences from singular black holes.

Findings

Displacement memory depends on the regularization parameter g and pulse height.

Regular black holes show distinct displacement memory compared to singular black holes.

Memory magnitude varies with parameters and is observable at large u.

Abstract

Displacement memory, induced by a wave pulse in a regular black hole spacetime, is studied using geodesic (timelike) separation and geodesic deviation. The presence of the wave pulse in such a black hole is modeled via a function $H(u)$ appearing in a restricted version of a generic Bondi-Sachs type line element. Choosing a sech-squared profile for $H(u)$, we first study (numerically) geodesic separation and geodesic deviation in a flat background. Thereafter, similar investigations are carried out in the presence of the black hole, but in regions far away from the vicinity of the horizon. Our results suggest the presence of a distinct displacement memory effect, which depends on the value of the regularisation parameter $g$ as well as the pulse height. Between different types of regular black holes, one notices parameter-dependent changes in the net displacement memory. Further, a clear difference in the magnitude of displacement memory (at large $u$) in regular and singular black holes is also visible in our numerical results.