Abstract

Gravitation theories selected by requiring that they have a unique anti-de Sitter vacuum with a fixed cosmological constant are studied. For a given dimension d, the Lagrangians under consideration are labeled by an integer k=1,2, . . . ,[(d-1)/2]. Black holes for each d and k are found and are used to rank these theories. A minimum possible size for a localized electrically charged source is predicted in the whole set of theories, except general relativity. It is found that the thermodynamic behavior falls into two classes: If d-2k=1, these solutions resemble the three dimensional black hole; otherwise, their behavior is similar to the Schwarzschild-AdS4 geometry. ©2000 The American Physical Society.