Compact stars in Energy-Momentum Squared Gravity

TL;DR

This paper explores how Energy-Momentum Squared Gravity (EMSG), a modification of general relativity, affects the structure and mass-radius relations of neutron stars, revealing potential deviations from GR in high-density regimes.

Contribution

The study derives the generalized TOV equations in EMSG, provides analytical and numerical solutions for neutron star models, and demonstrates EMSG's impact on neutron star masses and radii.

Findings

EMSG can produce larger or smaller neutron star masses depending on parameters.

High-mass neutron stars can exist in EMSG with ordinary equations of state.

Deviations from GR are significant in high curvature regimes within stars.

Abstract

A simple generalization to Einstein's general relativity (GR) was recently proposed which allows a correction term $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory. This theory is called Energy-Momentum Squared Gravity (EMSG) and introduces a new coupling parameter $\eta$. EMSG resolves the big bang singularity and has a viable sequence of cosmological epochs in its thermal history. {Interestingly, in the vacuum EMSG is equivalent to GR, and its effects appear only inside the matter-energy distribution. More specifically, its consequences appear in high curvature regime. Therefore it is natural to expect deviations form GR inside compact stars. In order to study spherically symmetric compact stars in EMSG, we find the relativistic governing equations. More specifically, we find the generalized version of the Tolman-Oppenheimer-Volkov equation in EMSG. Finally we present two analytical solutions, and two numerical solutions for the field equations. For obtaining the numerical solutions we use polytropic equation of state which is widely used to understand the internal structure of neutron stars in the literature. Eventually we find a mass-radius relation for neutron stars. Also, We found that EMSG, depending on the central pressure of the star and the magnitude of free parameter $\eta$, can lead to larger or smaller masses for neutron stars compared with GR. Existence of high-mass neutron stars with ordinary polytropic equation of state in EMSG is important in the sense that these stars exist in GR provided that one use exotic equation of states.