Thermodynamics of EMD-AdS black hole with deformed horizon

Abstract: We show that the horizon shapes of static Einstein-Maxwell-dilaton (EMD) black holes can be deformed through an approach analogous to those observed in novel topological black hole solutions supported by two massless axion fields. Particularly, the radial part of the spacetime remains unchanged, while the angular part has a non-constant Ricci scalar, signaling the presence of anisotropy. We further explore the implications of this anisotropy for the thermodynamic properties of the black hole. The validity of the Misner-Sharp (MS) mass and the unified first law are also addressed in this study.