Possible existence of stable compact stars in $\kappa(\mathcal{R},\mathcal{T})-$gravity

TL;DR

This paper derives new interior solutions for compact stars within $ abla( ext{R}, ext{T})$ gravity, demonstrating their physical viability and consistency with gravitational wave observations, thus suggesting the possible existence of stable compact stars in this modified gravity framework.

Contribution

The paper introduces the first interior solutions for compact stars in $ abla( ext{R}, ext{T})$ gravity, incorporating specific metric potentials and analyzing their physical properties.

Findings

Solutions satisfy energy, causality, and Bondi criteria.

Mass-radius curves align with GW 170817 constraints.

Solutions indicate possible stable compact stars in modified gravity.

Abstract

We present the first interior solutions representing compact stars in $\kappa(\mathcal{R},\mathcal{T})$ gravity, by solving the modified field equations in isotropic coordinates. Further, we have assumed the metric potentials in Schwarzschild's form and a few parameters along with the isotropic condition of pressure. For solving, we use specific choice of the running gravitational constant as $\kappa(\mathcal{R},\mathcal{T})=8\pi-\lambda \mathcal{T} ~~(G=\tilde{c}=1)$. Once arrived at the reduced field equations, we investigate two solutions with $c=1$ and $c \neq 1$, where $c$ denotes here another constant that should not be confused with the speed of light. Then, we investigate each solution by determining the thermodynamics variable {\it viz} pressure, density, speed of sound, and adiabatic index. We found that these solutions satisfy the Bondi criterion, causality condition, and energy conditions. We also found that the $M-R$ curves generated from these solutions satisfy the stringent constraints provided by the gravitational wave observations due to the neutron star merger GW 170817.