Black holes in 4D Einstein–Maxwell supergravity with power-law lagrangian deformations

We studied static, spherically symmetric black hole solutions in four-dimensional Einstein–Maxwell supergravity, generalized by a small power-law deformation of the conventional Lagrangian L of the form [Formula: see text], where [Formula: see text] parameterizes deviations from linear field dynamics, [Formula: see text] sets the characteristic energy scale of the deformation, and L is the standard Einstein–Hilbert plus Maxwell action. Working to first order in [Formula: see text], we derived the linearized field equations and obtained explicit expressions for the metric correction in Reissner–Nordström (RN) backgrounds. We computed the associated corrections to horizon radius, surface gravity, temperature, and Wald entropy, imposing the first law of thermodynamics to fix integration constants. The analysis is extended to asymptotically AdS black holes, extremal configurations exhibiting the attractor mechanism, and the regulated Schwarzschild limit. Our results demonstrate that the logarithmic corrections induced by the Lagrangian deformation lead to multiplicative modifications of the entropy and thermodynamic potentials, providing insights into quantum gravity corrections, higher-derivative interactions, and effective supergravity models.