Thermodynamical first laws of black holes in quadratically-extended gravities
Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical/toric/hyperbolic isometries in these theories. This allows us to derive/rederive the first laws for a wide range of black holes in literature. Furthermore, we construct many new exact solutions and obtain their first laws.