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 $$f(\mathcal{R},\mathcal{G},\mathcal{T})=\mathcal{R}+α\,\mathcal{G}+β\,\mathcal{T}$$ where $α$ and $β$ are parameters of suitable dimensionality,\footnote{$α$ has dimensions of $[L<sup>{2}]$ and $β$ carries units of $[N<sup>{-1}]$.} 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 $$α<em>{1}=α/R^{2},\qquad β</em>{1}=β/κ<sup>{2}$$ together with the compactness $C=2GM/(Rc<sup>{2})$. We constraint the two parameters $α$ and $β$ by matching the model with the mass and radius of pulsar \textit{U1724} requires restricting these parameters to $α<em>{1}=\pm0.023$ and $β</em>{1}=\pm0.001$, where $κ<sup>{2}=8πG/c<sup>{4}$ is the standard Einstein coupling. The resulting stellar configuration satisfies the causal bound on the radial sound speed, $c_{s}<sup>{2}&lt;c<sup>{2}/3$, distinguishing it from the corresponding behaviour in general relativity.