Implication of f(ℛ,ℒm,𝒯 ) gravity on the anisotropic compact stars and mass-radius relations under NICER radii measurements of PSR J0740+6620

In this work, we have investigated the consequences happen to a configuration of a neutron star when gravity itself is modified by a non-minimal coupling between matter and geometry. Particularly, we explore a new exact analytical solution for anisotropic compact stars using the Buchdahl metric potential within [Formula: see text] gravity. The present model reveals a remarkable hydrostatic equilibrium where the inward gravitational pull is counterbalanced not only by pressure gradients and anisotropy but also by a novel curvature-matter coupling force. The predicted central energy densities range from [Formula: see text] to [Formula: see text], while central pressures span [Formula: see text] to [Formula: see text]. Stability of the stellar configuration is assured with adiabatic indices [Formula: see text] to [Formula: see text] exceeding the [Formula: see text] threshold, sound speeds [Formula: see text], and the cracking condition satisfied throughout. Remarkably, mass-radius relation presented in the present model predicts radii of PSR J1903+327, PSR J0740+6620, PSR J1614-2230 and PSR J2215+5135. We obtain radius of PSR J0740+6620 to be [Formula: see text] km for mass [Formula: see text] based on the data obtained from the [Formula: see text] curves restricting the [Formula: see text] parameters space so that central density is of the order of [Formula: see text] for the sustainability of high mass in the massive pulsars. The present model predictions are in good agreement with the lower bounds of the observed radii values of PSR J0740+6620 by the recent NICER measurements. The current findings establish [Formula: see text] gravity as a compelling framework for describing compact astrophysical objects, providing a robust foundation for future multimessenger tests of strong-field gravity.