Abstract <p> We explore isotropic charged compact stars within the framework of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(R,\mathcal T\mkern1.5mu)\)</EquationSource> </InlineEquation> gravity, employing a novel approach grounded in conformal Killing vectors to model strange stars and analyze their physical viability and stability. Utilizing the simplified MIT bag equation of state (EOS) for quark matter, we derive exact solutions to the Einstein field equations for observed masses of strange star candidates, with LMC X-<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(4\)</EquationSource> </InlineEquation> as a representative case. The parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varpi\)</EquationSource> </InlineEquation> (ranging from <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(-1.6\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(1.6\)</EquationSource> </InlineEquation>) governs modifications in the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(f(R,\mathcal T\mkern1.5mu)\)</EquationSource> </InlineEquation> gravity formalism, enabling systematic investigation of key properties. Our results confirm singularity-free metric potentials, monotonically decreasing effective energy density (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\rho^{\mathrm{ef}}\)</EquationSource> </InlineEquation>) and pressure (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(p^{\mathrm{ef}}\)</EquationSource> </InlineEquation>), and adherence to energy conditions across all <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\varpi\)</EquationSource> </InlineEquation> values. The mass–radius relationship, analyzed for a fixed bag constant <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\mathcal B=83\,\mathrm{MeV}/\mathrm{fm}^3\)</EquationSource> </InlineEquation>, reveals that maximum mass points increase with <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\varpi\)</EquationSource> </InlineEquation>. A prescribed density profile (free of central singularities) combined with the MIT bag EOS yields exact solutions to the modified Tolman–Oppenheimer–Volkoff equations, circumventing numerical complexities. Stability analysis demonstrates equilibrium via force balance, with an emergent force <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(F_{\mathrm m}\)</EquationSource> </InlineEquation> in <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(f(R,\mathcal T\mkern1.5mu)\)</EquationSource> </InlineEquation> gravity: repulsive (outward) for <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\varpi<0\)</EquationSource> </InlineEquation> and attractive (inward) for <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\varpi>0\)</EquationSource> </InlineEquation>. Stability is further validated by subluminal sound speeds (<InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(v_{\mathrm s}^2\in[0,1]\)</EquationSource> </InlineEquation>) and adiabatic indices (<InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(\Gamma>4/3\)</EquationSource> </InlineEquation>). High surface/central densities and redshifts (<InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(\sim 0.23\)</EquationSource> </InlineEquation>–<InlineEquation ID="IEq20"> <EquationSource Format="TEX">\(0.36\)</EquationSource> </InlineEquation>) align with strange quark star characteristics, while all <InlineEquation ID="IEq21"> <EquationSource Format="TEX">\(2M/\mathcal R\)</EquationSource> </InlineEquation> values remain below the Buchdahl limit. The results establish a robust, stable stellar model for strange stars, leveraging conformal symmetries and <InlineEquation ID="IEq22"> <EquationSource Format="TEX">\(f(R,\mathcal T\mkern1.5mu)\)</EquationSource> </InlineEquation> gravity, and provide a foundation for future studies on alternative density profiles in modified gravity. </p>

Isotropic charged compact stars in \(f(R,\mathcal T\mkern1.5mu)\) gravity: A conformal Killing vector approach to stability, exact solutions, and strange star candidates

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发表日期：

2025年11月25日

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I. G. Salako,
H. S. Ahouannou,
F. Mavoa,
V. A. Monwanou

摘要

Abstract

We explore isotropic charged compact stars within the framework of \(f(R,\mathcal T\mkern1.5mu)\) gravity, employing a novel approach grounded in conformal Killing vectors to model strange stars and analyze their physical viability and stability. Utilizing the simplified MIT bag equation of state (EOS) for quark matter, we derive exact solutions to the Einstein field equations for observed masses of strange star candidates, with LMC X- \(4\) as a representative case. The parameter \(\varpi\) (ranging from \(-1.6\) to \(1.6\) ) governs modifications in the \(f(R,\mathcal T\mkern1.5mu)\) gravity formalism, enabling systematic investigation of key properties. Our results confirm singularity-free metric potentials, monotonically decreasing effective energy density ( \(\rho^{\mathrm{ef}}\) ) and pressure ( \(p^{\mathrm{ef}}\) ), and adherence to energy conditions across all \(\varpi\) values. The mass–radius relationship, analyzed for a fixed bag constant \(\mathcal B=83\,\mathrm{MeV}/\mathrm{fm}^3\) , reveals that maximum mass points increase with \(\varpi\) . A prescribed density profile (free of central singularities) combined with the MIT bag EOS yields exact solutions to the modified Tolman–Oppenheimer–Volkoff equations, circumventing numerical complexities. Stability analysis demonstrates equilibrium via force balance, with an emergent force \(F_{\mathrm m}\) in \(f(R,\mathcal T\mkern1.5mu)\) gravity: repulsive (outward) for \(\varpi<0\) and attractive (inward) for \(\varpi>0\) . Stability is further validated by subluminal sound speeds ( \(v_{\mathrm s}^2\in[0,1]\) ) and adiabatic indices ( \(\Gamma>4/3\) ). High surface/central densities and redshifts ( \(\sim 0.23\) – \(0.36\) ) align with strange quark star characteristics, while all \(2M/\mathcal R\) values remain below the Buchdahl limit. The results establish a robust, stable stellar model for strange stars, leveraging conformal symmetries and \(f(R,\mathcal T\mkern1.5mu)\) gravity, and provide a foundation for future studies on alternative density profiles in modified gravity.