The thermodynamic properties of black holes in Lovelock gravity are examined. In particular, the case of the Einstein Lagrangian plus the four-dimensional Euler density is discussed in detail. In five dimensions, one finds that the specific heat of a black hole becomes positive at small mass, allowing the black hole to achieve stable equilibrium with its environment and giving it an infinite lifetime. This behavior is not universal, however, but it always occurs in 2k+1 dimensions for a Lovelock theory including the 2k-dimensional Euler density. For theories including six-derivative or higher-order interactions, black holes with degenerate zero-temperature horizons are also possible.

• Received 25 April 1988

DOI:https://doi.org/10.1103/PhysRevD.38.2434