Curvature Effect on the Speed of Sound

TL;DR

This paper derives a covariant wave equation in general relativity to study how spacetime curvature affects the speed of sound in neutron stars, revealing a reduction in sound speed due to gravity.

Contribution

It introduces a covariant formalism for the sound wave equation in curved spacetime, showing how gravity influences the effective speed of sound in astrophysical objects.

Findings

Curvature reduces the effective sound speed inside neutron stars.

The formalism allows visualization of mode amplitude attenuation due to gravity.

The wave equation is modified in the general relativistic context.

Abstract

The speed of sound refers to the rate at which information travels from one point to another. It is a positive quantity and bounded by causality. It is defined as the rate of change of pressure with respect to the system's density. In this article, we derive a covariant equation for the sound wave and demonstrate how the wave equation is modified in the general relativistic formalism. One can then define an effective speed of sound by attenuating the usual definition of sound speed with the gravitational metric potential. The general relativistic curvature effect is observed to reduce the speed of sound when computed inside a neutron star. This effectively makes the star relatively softer (according to the equation of state). The change in the effective sound speed can be easily visualised if one redefines the non-radial modes in terms of it. The modes do not change, but the space-time curvature reduces the amplitude of the oscillation modes. The formalism is suited for studying astrophysical compact objects.