Black Holes in Higher Curvature Gravity1

The idea that the Einstein action should be modified by the addition of interactions involving higher powers of the Riemann curvature tensor has a long history stretching back to the early days of general relativity. Such higher curvature theories originally appeared in proposals by Weyl and Eddington for a geometric unification of electromagnetism and gravity[1]. Much later, interest arose in higher derivative theories of gravity because they provided renormalizable quantum field theories[2, 3]. Unfortunately, the new massive spin-two excitations, which tame the ultraviolet divergences in such theories, result in the instability of the classical theory[4] and the loss of unitarity in the quantum theory[3, 5]. While higher curvature theories have thus proven inadequate as the foundation of quantum gravity, they still have a role to play within the modern paradigm of effective field theories[6]. Irrespective of the fundamental nature of quantum gravity, there should be a low energy effective action which describes the dynamics of a “background metric field” for sufficiently weak curvatures and sufficiently long distances. On general grounds, this effective gravity action will consist of the usual Einstein action plus a series of covariant, higher-dimension interactions, i.e., higher curvature terms, and also higher derivative terms involving the “low-energy” matter fields. The appearance of such interactions can be seen, for example, in the renormalization of quantum field theory in curved space-time[7], or in the construction of low-energy effective