Dynamical excitation of space-time modes of compact objects

TL;DR

This paper investigates how Gaussian gravitational wave pulses excite space-time modes in non-rotating stars and black holes, highlighting the dependence on pulse width and implications for distinguishing compact objects.

Contribution

It provides a detailed analysis of the excitation of $w$-modes in stars and black holes using perturbative methods, comparing the effects of pulse width on mode excitation.

Findings

Narrow pulses strongly excite $w$-modes.

Wide pulses lead to tail-dominated signals, suppressing quasi-normal modes.

Results aid comparison between perturbative and nonlinear numerical simulations.

Abstract

We discuss, in the perturbative regime, the scattering of Gaussian pulses of odd-parity gravitational radiation off a non-rotating relativistic star and a Schwarzschild Black Hole. We focus on the excitation of the $w$-modes of the star as a function of the width $b$ of the pulse and we contrast it with the outcome of a Schwarzschild Black Hole of the same mass. For sufficiently narrow values of $b$, the waveforms are dominated by characteristic space-time modes. On the other hand, for sufficiently large values of $b$ the backscattered signal is dominated by the tail of the Regge-Wheeler potential, the quasi-normal modes are not excited and the nature of the central object cannot be established. We view this work as a useful contribution to the comparison between perturbative results and forthcoming $w$-mode 3D-nonlinear numerical simulation.