White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory $f(R, T, L_m) = R + \alpha T L_m$, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: $L_m = p$ and $L_m = -\rho$. We show that the extra $\alpha TL_m$ term significantly alters the mass-radius relation of WDs, especially at high central densities $( \rho_c \gtrsim 10^8 - 10^9\,\rm g/cm^3)$, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter $\alpha$, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that $f(R,T,L_m)$ gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter $\alpha$ for the two choices of the Lagrangian density $L_m$.