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

Abstract

Abstract We investigate the properties of compact objects in the f(Q, T) theory, where $$\mathcal {Q}$$ Q is the non-metricity scalar and $${ \mathcal {T}}$$ 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 $$f(\mathcal {Q}, { \mathcal {T}})=\mathcal {Q}+\psi { \mathcal {T}}$$ f ( Q , T ) = Q + ψ T , where $$\psi $$ ψ represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021, $$\psi $$ ψ is set to a maximum negative value of $$\psi _1=\psi / \kappa ^2=-0.04$$ ψ 1 = ψ / κ 2 = - 0.04 , where $$\kappa ^2$$ κ 2 is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition $$c_s^2\le \frac{c^2}{3}$$ c s 2 ≤ 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 $$\psi $$ ψ 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 $$\psi $$ ψ 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 $$f(\mathcal {Q}, { \mathcal {T}})$$ f ( Q , T ) theory and for GR is $$C = 0.514$$ C = 0.514 and 0.419, respectively, with the $$f(\mathcal {Q}, { \mathcal {T}})$$ f ( Q , T ) prediction about $$10\%$$ 10 % higher than the GR one. Assuming a surface density at saturation nuclear density of $$\rho _{\text {nuc}} = 4\times 10^{14}~\hbox {g}/\hbox {cm}^3$$ ρ nuc = 4 × 10 14 g / cm 3 , the maximum mass of the star is $$4.66 M_\odot $$ 4.66 M ⊙ , with a radius of 14.9 km.