One entropy function to rule them all…

Abstract

We study the entropy of extremal four dimensional black holes and five dimensional black holes and black rings is a unified framework using Sen's entropy function and dimensional reduction. The five dimensional black holes and black rings we consider project down to either static or stationary black holes in four dimensions. The analysis is done in the context of two derivative gravity coupled to abelian gauge fields and neutral scalar fields. We apply this formalism to various examples including U (1) 3 minimal supergravity.

Heterotic black holes

“…For extremal black holes one expects AdS 2 × S 2 near-horizon geometry [37,38,39] which in the present case is given by:…”

Properties of rotating Einstein-Maxwell-dilaton black holes in odd dimensions

“…So there are seven constants to be determined. The near-horizon formalism allows us to extract information about the global solutions from the near-horizon geometry 12,13 , such as the angular momentum, the electric charge, the horizon area or the horizon angular momentum. Other quantities such as the mass or the horizon angular velocity cannot be inferred from this formalism.…”

Black Holes in Higher Dimensions (Black Strings and Black Rings)

“…The general set of analytical Einstein-Maxwelldilaton black holes can be constructed by employing a Kaluza-Klein reduction for a particular value of the dilaton coupling constant, h = h KK 64-67 . For different values of the dilaton coupling constant h, however, one either has to employ perturbative techniques [68][69][70][71][72][73][74] or perform a numerical analysis [75][76][77][78] , while for extremal black holes one may, in addition, resort to the near-horizon formalism to gain understanding of the properties of these black holes [79][80][81][82] . Specializing to black holes with equal angular momenta, Francisco NavarroLérida explained, that in odd-D dimensions this leads to an enhancement of the symmetry of the solutions, and a substantial simplification of the equations to cohomogeneity-1, such that only ODEs and not PDEs must be considered 76 , and that in the near-horizon formalism the resulting formulae are all analytical.…”