Novel topological black holes from thermodynamics and deforming horizons

Two novel topological black hole exact solutions with unusual shapes of horizons in the simplest holographic axions model, the four-dimensional Einstein-Maxwell-axions theory, are constructed. We draw embedding diagrams in various situations to display unusual shapes of novel black holes. To understand their thermodynamics from the quasilocal aspect, we rederive the unified first law and the Misner-Sharp mass from the Einstein equation for the spacetime as a warped product {M} (₂) ^{M} (₃-₂). The Ricci scalar ^R of the submanifold ^{M} (₃-₂) can be a nonconstant. We further improve the thermodynamics method based on the unified first law. Such a method simplifies constructing solutions and hints at generalization to higher dimensions. Moreover, we apply the unified first law to discuss black hole thermodynamics.