Constraining linear form of $f(\mathcal{R,G,T})$ gravity from astrophysical observations of the Pulsar U1724

TL;DR

This paper investigates the internal structure of compact stars within a modified gravity framework characterized by a linear function of curvature, Gauss-Bonnet, and matter trace, constrained by pulsar observations to test gravity theories.

Contribution

It derives an exact analytic solution for static anisotropic stars in $f( ext{R,G,T})$ gravity with a linear form, constraining model parameters using pulsar data.

Findings

Model parameters constrained to $ ext{alpha}_1= ext{pm}0.023$, $ ext{beta}_1= ext{pm}0.001$ from pulsar U1724 data.

Stellar models satisfy the causal bound on sound speed, differing from general relativity.

Provides a new analytic solution for anisotropic stars in extended gravity theories.

Abstract

In this work we examine the internal structure of compact stars within an extended gravitational framework described by the function $f(\mathcal{R},\mathcal{G},\mathcal{T})$. Throughout this work, the quantity $\mathcal{R}$ refers to the curvature scalar formed from the Ricci tensor. The term $\mathcal{G}$ denotes the Gauss--Bonnet curvature invariant, while $\mathcal{T}$ corresponds to the trace obtained by contracting the matter energy-momentum tensor. Our analysis is directed toward massive radio pulsars with masses above $1.8\,M_{\odot}$, which provide an exceptional testing ground for gravity under conditions inaccessible to laboratory experiments. Adopting the linear form $f(\mathcal{R},\mathcal{G},\mathcal{T})=\mathcal{R}+\alpha\,\mathcal{G}+\beta\,\mathcal{T}$ where $\alpha$ and $\beta$ are parameters of suitable dimensionality,\footnote{$\alpha$ has dimensions of $[L^{2}]$ and $\beta$ carries units of $[N^{-1}]$.} we obtain an exact analytic solution for static anisotropic stellar matter in hydrostatic equilibrium. This solution allows all physical quantities to be expressed in terms of the dimensionless parameters $ \alpha_{1}=\alpha/R^{2},\qquad \beta_{1}=\beta/\kappa^{2}$ together with the compactness $C=2GM/(Rc^{2})$. We constraint the two parameters $\alpha$ and $\beta$ by matching the model with the mass and radius of pulsar \textit{U1724} requires restricting these parameters to $\alpha_{1}=\pm0.023$ and $\beta_{1}=\pm0.001$, where $\kappa^{2}=8\pi G/c^{4}$ is the standard Einstein coupling. The resulting stellar configuration satisfies the causal bound on the radial sound speed, $c_{s}^{2}<c^{2}/3$, distinguishing it from the corresponding behaviour in general relativity.