Constraining Matter-Geometry Coupling: NICER and LIGO/Virgo Insights into Anisotropic Pulsars via <i>f</i> ( <i>R</i> , <i>T</i> ) Gravity

This investigation presents a thorough examination of massive anisotropic pulsar configurations within the modified gravitational framework of [Formula: see text], where the parameter [Formula: see text] quantifies the interaction strength between material content and spacetime geometry. Through derivation of modified Einstein field equations appropriate for static spherically symmetric spacetimes, combined with a modified Chaplygin description for ultra-dense nuclear matter, we extend prior investigations by implementing systematic Bayesian calibration utilizing contemporary NICER observations of PSR J0348+0432 ([Formula: see text]) and PSR J0030+0451 ([Formula: see text], [Formula: see text] km), alongside gravitational wave constraints from GW170817 and GW190814 events. Our analysis demonstrates that negative coupling values ([Formula: see text]) generate repulsive modifications within the field equations that counterbalance gravitational attraction, thereby enabling stable ultra-dense configurations. Central energy densities span [Formula: see text] g cm[Formula: see text] to [Formula: see text] g cm[Formula: see text], with surface densities approximating [Formula: see text] g cm[Formula: see text]. The resulting mass-radius relationships demonstrate remarkable concordance with observational constraints from NICER and LIGO/Virgo. Through causality considerations, stability requirements, and observational consistency, we constrain the coupling parameter to [Formula: see text]. All energy conditions remain satisfied throughout stellar interiors, while the Harrison-Zeldovich-Novikov stability criterion confirms configuration stability. The adiabatic index consistently exceeds the critical threshold [Formula: see text], and gravitational redshift values ([Formula: see text]) reside within observationally permissible ranges. These findings suggest that [Formula: see text] gravity offers a viable theoretical framework for describing ultra-dense pulsar configurations, with the coupling constant naturally functioning as an effective phenomenological representation of dark matter interactions.