A Study of Compact Stellar Objects in <i>f</i>(<i>R</i>, <i>T</i>) Theory of Gravity

In this paper, we investigate the stability and feasibility of an anisotropic stellar model under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity that embraces the Karmarkar condition. In order to develop the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity model, the functional form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> is taken into consideration as the linear function of the trace of the energy-momentum tensor <i>T</i> and the Ricci scalar <i>R</i>, respectively. This study proposes a well-known form of the radial metric function and finds another metric function by employing the Karmakar condition, which provides the exact solution to the field equation. The expression of the model parameters is derived by matching the obtained interior solutions with the Schwarzschild exterior metric over the bounding surface of a celestial object, along with the requirement that the radial pressure vanish at the boundary. The current estimated data of the star, pulsar 4U1608-52, is used to graphically explore the model. The physical attributes of the celestial object are thoroughly examined within the framework of the present model. Adjusting the model parameter, a detailed analysis of the stability criterion is presented that involves the adiabatic index, the Herrera cracking technique, and the causality condition. Furthermore, the Tolman–Oppenheimer–Volkhoff equation is used to analyze the stellar model’s equilibrium state. In order to maintain the stability condition of the anisotropic stellar structure, a suitable range for the model parameter is determined by the graphical analysis of the present model in this study. In addition, the numerical values of the physical parameters related to the compact stars Her X-1, LMC X-4, Cen X-3 and KS1731-207 are used to examine the model solution within the desired range of the model parameter.