Compact anisotropic stellar model in Tolman–Kuchowicz spacetime in extended theory of gravity

The study of compact stellar systems in extended theories of gravity is crucial for understanding the behaviour and nature of the matter within these systems. We systematically study an anisotropic compact stellar model utilizing a Tolman–Kuchowicz spacetime configuration in the simplest form of f(R, T)-gravity where R is the Ricci scalar and T is the trace of the stress-energy tensor. The interior spacetime of the system is matched with the Schwarzschild exterior solutions using which the associated constants of the model are determined. For different values of the model parameters associated with the model, the physical variables are studied for a few selected compact star candidates Swift J1818.0-1607, PSR J1614-2230 and PSR J0348+0432. To physically verify the solutions, we tested the presence of a singularity using the Kretschmann scalar, which showed that the compact stellar model is non-singular at the centre. The equation of state is then determined numerically for all the compact star candidates and for some selected values of the model parameters which favours non-linear equation of state for radial and tangential matter profiles. The examination of the energy conditions indicates that the fluid distribution in the system is non-exotic. Following this, we have also studied the mass-radius relationship, surface redshift, gravitational redshift and the stability conditions based on sound speed, relativistic adiabatic index, Harrison-Zeldovich stability and TOV equation. The results indicate that the compact star system obeys the required stability criteria.