Gravitational Waves in Scalar–Tensor–Vector Gravity Theory

Yunqi Liu,Yungui Gong,Bin Wang,Wei-Liang Qian

doi:10.3390/universe7010009

Abstract

In this paper, we study the properties of gravitational waves in the scalar–tensor–vector gravity theory. The polarizations of the gravitational waves are investigated by analyzing the relative motion of the test particles. It is found that the interaction between the matter and vector field in the theory leads to two additional transverse polarization modes. By making use of the polarization content, the stress-energy pseudo-tensor is calculated by employing the perturbed equation method. Additionally, the relaxed field equation for the modified gravity in question is derived by using the Landau–Lifshitz formalism suitable to systems with non-negligible self-gravity.

Highlights

The recent observation of gravitational waves (GWs) by the LIGO and Virgo Scientific Collaboration opens up a new avenue to explore gravitational physics from an entirely new perspective [1,2,3,4,5,6,7]
The present paper is dedicated to studying various aspects of the GWs in a modified theory of gravity, namely, the Scalar–Tensor–Vector gravity (STVG) theory
As the model is shown to be in good agreement in the context of the weak field, it is meaningful to further investigate its validity for the strong field, in terms of the GWs

Summary

Introduction

The recent observation of gravitational waves (GWs) by the LIGO and Virgo Scientific Collaboration opens up a new avenue to explore gravitational physics from an entirely new perspective [1,2,3,4,5,6,7]. One commonly employed approach is to study the polarization of weak, plane, and null GWs by using Newman-Penrose (NP) formalism [8,12,24,25,26,27,28] Another method consists of reducing the metric into irreducible components and rewriting the linearized gravitational equations into the independent scalar, vector, and tensorial parts [29,30]. Besides the properties of the plane GW, we are interested in the “relaxed gravitational equation” which could be used to describe systems with with non-negligible self-gravity Such results may serve to futher study of the binary star systems or those with non-linear GW memory effect [40,41,42,43], which subsequently build up the foundation for future investigations. One assumes that self-interaction potentials Vφ, VG, and Vμ vanish in the following discussions

Linearized Field Equations

The Relative Motion of Neighboring Particles

The Stress-Energy Pseudo-Tensor

Extension to Sources with Non-Negligible Self-Gravity

Concluding Remarks