Structure, maximum mass, and stability of compact stars in gravity

G. G. L. Nashed; Tiberiu Harko

doi:10.1140/epjc/s10052-024-13436-8

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 1086
https://doi.org/10.1140/epjc/s10052-024-13436-8

Regular Article

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

G. G. L. Nashed¹ and Tiberiu Harko²^,3^b

¹ Centre for Theoretical Physics, The British University in Egypt El Sherouk City, Suez Desert Road, 11837, Cairo, Egypt
² Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
³ Astronomical Observatory, 19 Ciresilor Street, 400487, Cluj-Napoca, Romania

^b tiberiu.harko@aira.astro.ro

Received: 2 July 2024
Accepted: 29 September 2024
Published online: 19 October 2024

Abstract

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

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Funded by SCOAP³.

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

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