Thermodynamical First Laws of Black Holes in Quadratically-Extended Gravities

TL;DR

This paper derives thermodynamical first laws for black holes in quadratic curvature extended gravities, introduces new solutions, and applies the Wald formalism to a broad class of spacetimes.

Contribution

It provides a unified formula for black hole thermodynamics in extended gravities and constructs new exact solutions with their first laws.

Findings

Derived explicit first law formulas for various black holes.

Constructed new exact black hole solutions.

Unified approach applicable to multiple spacetime asymptotics.

Abstract

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.