Structure, maximum mass, and stability of compact stars in \(f(\mathcal {Q,T})\) gravity

Abstract

We investigate the properties of compact objects in the f(Q, T) theory, where \(\mathcal {Q}\) is the non-metricity scalar and \({ \mathcal {T}}\) is the trace of the energy–momentum tensor. We derive an interior analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the linear form of \(f(\mathcal {Q}, { \mathcal {T}})=\mathcal {Q}+\psi { \mathcal {T}}\), where \(\psi \) represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021, \(\psi \) is set to a maximum negative value of \(\psi _1=\psi / \kappa ^2=-0.04\), where \(\kappa ^2\) is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition \(c_s^2\le \frac{c^2}{3}\). The effective equation of state is similar to the quark matter equation of state, and involves the presence of an effective bag constant. When \(\psi \) is negative, the star has a slightly larger size as compared to GR stars with the same mass. The difference in the predicted star size between the theory with a negative \(\psi \) and GR for the same mass is attributed to an additional force appearing in the hydrodynamic equilibrium equation. The maximum compactness allowed by the strong energy condition for \(f(\mathcal {Q}, { \mathcal {T}})\) theory and for GR is \(C = 0.514\) and 0.419, respectively, with the \(f(\mathcal {Q}, { \mathcal {T}})\) prediction about \(10\%\) higher than the GR one. Assuming a surface density at saturation nuclear density of \(\rho _{\text {nuc}} = 4\times 10^{14}~\hbox {g}/\hbox {cm}^3\), the maximum mass of the star is \(4.66 M_\odot \), with a radius of 14.9 km.