Probing Tensor-Vector-Scalar Theory with Gravitational Wave Asteroseismology

TL;DR

This paper investigates how gravitational wave asteroseismology can test TeVeS gravity by analyzing axial w modes in neutron stars, revealing differences from general relativity that could be observed.

Contribution

It derives perturbation equations for relativistic stars in TeVeS, focusing on axial modes and their dependence on stellar properties, highlighting observable differences from GR.

Findings

Axial w mode frequencies are largely independent of the equation of state.

Frequencies depend on TeVeS parameters and differ from GR predictions.

Observations of gravitational waves could distinguish TeVeS from GR.

Abstract

In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime ($w$ modes), are independent from the perturbations of scalar field and the effects of scalar field can be mounted only via the background properties. Using two different equations of state, we calculate the complex eigenfrequencies of axial $w$ modes and find that the dependences of frequencies on the stellar compactness are almost independent from the adopted equation of state and the parameter in TeVeS. Additionally, these dependences of frequencies of axial $w$ modes in TeVeS is obviously different from those expected in the general relativity. Thus the direct observations of gravitational waves could reveal the gravitational theory in the strong-field regime.