Radiating Stellar Structures in f ( R , Σ) Gravity: A Limiting Case of the f ( R , Σ, T ) Framework

This paper presents a theoretical study of ultra-dense, radiating stars within an advanced framework of modified gravity, known as f(R, Σ, T) gravity. This theory extends Einstein’s General Relativity by introducing a more complex interaction between the curvature of spacetime, its torsion, and the internal properties of matter. To manage the formidable mathematical complexity of this theory, the authors impose a specific symmetry on the spacetime structure, namely a conformal symmetry. This powerful simplifying assumption allows for the derivation of an exact, analytical solution describing the star’s interior geometry and physical properties. The stellar matter is modeled as a perfect fluid dominated by radiation pressure, following the well-established relationship p = ρ/3, where p is the pressure and ρ is the energy density. This choice is particularly relevant for understanding extremely hot and luminous astrophysical objects. The key findings of the model are that the solution provides complete mathematical descriptions for how the star’s density and pressure change from its core to its surface. The star’s stability against gravitational collapse is governed by a balance between three forces: the inward pull of gravity, the outward push from the pressure gradient, and a novel “extra force” that arises solely from the new matter-geometry coupling in the modified gravity theory. A critical parameter, b, controls the deviation from standard physics. When b = 0, the model seamlessly reduces to General Relativity, and the extra force disappears. For non-zero values of b, this parameter significantly alters the star’s internal structure. For positive b, the gravitational attraction is stronger, requiring a much steeper pressure gradient to maintain equilibrium. In extreme cases, positive b can lead to regions of negative energy density, which violates fundamental energy conditions and suggests that such parameter ranges may be unphysical. The model is designed to be tested against real astrophysical data. The derived formulas allow for the translation of observed properties, such as a star’s mass and radius, into constraints on the theory’s free parameters. In conclusion, this work provides a robust and tractable model for exploring the properties of compact stars in a sophisticated modified gravity theory. It highlights how such theories can profoundly alter our understanding of stellar interiors and offers a clear pathway for testing these theoretical predictions against modern astrophysical observations.