Black hole entropy function and the attractor mechanism in higher derivative gravity

Abstract

We study extremal black hole solutions in D dimensions with near horizon geometry AdS 2 × S D−2 in higher derivative gravity coupled to other scalar, vector and antisymmetric tensor fields. We define an entropy function by integrating the Lagrangian density over S D−2 for a general AdS 2 × S D−2 background, taking the Legendre transform of the resulting function with respect to the parameters labelling the electric fields, and multiplying the result by a factor of 2π. We show that the values of the scalar fields at the horizon as well as the sizes of AdS 2 and S D−2 are determined by extremizing this entropy function with respect to the corresponding parameters, and the entropy of the black hole is given by the value of the entropy function at this extremum. Our analysis relies on the analysis of the equations of motion and does not directly make use of supersymmetry or specific structure of the higher derivative terms.

Partition functions and elliptic genera from supergravity

“…In the last few years there has been much work (including [1,2,3,4,5]) on refining this identification to include the sub-leading asymptotics as well. On the black hole side this requires the inclusion of higher order spacetime effects, such as higher derivative corrections to the action.…”

“…On the black hole side this requires the inclusion of higher order spacetime effects, such as higher derivative corrections to the action. In favorable cases one has sufficient control to compute both sides of (1.1) beyond leading order and verify that the equality is upheld [1,2,3,4,5].…”

On attractor mechanism ofAdS4black holes

“…Since the effective potential method and entropy function formalism are equivalent in the near horizon limit, 4 we prefer to use the entropy function of Sen [16] 5 to prove the existence of regular extremal black holes with finite horizon area when P = 0.…”

Non-supersymmetric Attractors in Symmetric Coset Spaces

“…In 2005, Sen showed that all extremal black holes, both supersymmetric and non-supersymmetric (non-BPS), exhibit attractor behavior [2]: it is a result of the near-horizon geometry of extremal black holes, rather than supersymmetry. Since then, non-BPS attractors have been a very active field of research (see for instance [3,4,5,6,7,8,9,10,11,12,13,14,15]).…”