Radiative Falloff in Neutron Star Spacetimes

TL;DR

This study investigates how scalar waves decay over time in neutron star spacetimes, revealing different regimes of wave reflection and decay patterns depending on the star's compaction, with implications for understanding neutron star and black hole signals.

Contribution

It provides a systematic analysis of late-time wave tails in neutron star spacetimes across various compactions, highlighting the transition to black hole-like decay in the ultra-relativistic limit.

Findings

Distinct wave reflection regimes identified based on star compaction

Quasi-periodic peaks caused by wave bouncing inside the star

Power-law decay tails similar to black holes in the ultra-relativistic limit

Abstract

We systematically study late-time tails of scalar waves propagating in neutron star spacetimes. We consider uniform density neutron stars, for which the background spacetime is analytic and the compaction of the star can be varied continously between the Newtonian limit 2M/R << 1 and the relativistic Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off neutron stars of different compactions 2M/R and find that a Newtonian, an intermediate, and a highly relativistic regime can be clearly distinguished. In the highly relativistic regime, the reflected signal is dominated by quasi-periodic peaks, which originate from the wave packet bouncing back and forth between the center of the star and the maximum of the background curvature potential at R ~ 3 M. Between these peaks, the field decays according to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between the center and the maximum or the curvature potential grows without bound, so that the first peak arrives only at infinitely late time. The modes of neutron stars can therefore no longer be excited in the ultra-relativistic limit, and it is in this sense that the late-time radiative decay from neutron stars looses all its features and gives rise to power-law tails reminiscent of Schwarzschild black holes.