Echoes of axial gravitational perturbations in stars of uniform density

TL;DR

This paper develops a finite difference scheme to analyze axial gravitational perturbations in compact stars and black holes, revealing echoes in stellar oscillations caused by gravitational wave reflections within the star.

Contribution

It introduces an alternative numerical method for studying gravitational echoes in stars and black holes, emphasizing causality and wave reflections within stellar structures.

Findings

Echoes are observed in gravitational wave signals from uniform-density stars.

The scheme effectively distinguishes between reflected and transmitted wave components.

Quasinormal modes in stars can produce observable gravitational wave echoes.

Abstract

This work investigates the echoes in axial gravitational perturbations in compact objects. To this end, we propose an alternative scheme of the finite difference method implemented in two coordinate systems, where the initial conditions are placed on the axis of the tortoise coordinate with appropriate boundary conditions that fully respect the causality. The scheme is then employed to study the temporal profiles of the quasinormal oscillations in the Schwarzschild black hole and the uniform-density stars. When presented in a two-dimensional evolution profile, the resulting ringdown waveforms in the black hole metric are split into the reflected and transmitted waves as the initial perturbations evolve and collide with the peak of the effective potential. On the other hand, for compact stars, quasinormal oscillations might be characterized by echoes. Consistent with the causality arguments, the phenomenon is produced by the gravitational waves bouncing between the divergent potential at the star's center and the peak of the effective potential. The implications of the present study are also discussed.