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