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

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.