Gravitational wave memory in wormhole spacetimes

TL;DR

This paper investigates gravitational wave memory effects in a novel class of braneworld wormholes that do not require exotic matter, revealing unique signatures influenced by extra dimensions and wormhole geometry.

Contribution

It introduces a new class of traversable wormholes without exotic matter and analyzes their gravitational wave memory effects using geodesic and Bondi-Sachs formalisms.

Findings

Memory effects include displacement and velocity changes in geodesics.

Memory effects at null infinity show a change in Bondi mass after gravitational wave bursts.

Extra dimensions and wormhole geometry influence the memory signatures.

Abstract

Gravitational wave memory is studied in the context of a certain class of braneworld wormholes. Unlike other wormhole geometries, this novel class of wormholes do not require any exotic matter fields for its traversability. First, we study geodesics in this wormhole spacetime, in the presence of a gravitational wave pulse. The resulting evolution of the geodesic separation shows the presence of displacement and velocity memory effects. Motivated by the same, we study the memory effects at null infinity using the Bondi-Sachs formalism, adapted for braneworld wormhole. Our analysis provides a non-trivial change of the Bondi mass after the passage of a burst of gravitational radiation and hence manifests the memory effect at null infinity. In both of these exercises, the presence of extra dimension and the wormhole nature of the spacetime geometry gets imprinted in the memory effect. Since future gravitational wave detectors will be able to probe the memory effect, the present work provides another avenue to search for compact objects other than black holes.