Abstract
We show the equality between macroscopic and microscopic (statistical) black hole entropy for a class of four dimensional non-supersymmetric black holes in $$ \mathcal{N} $$ = 2 supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of [1], connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.
Highlights
We show the equality between macroscopic and microscopic black hole entropy for a class of four dimensional non-supersymmetric black holes in N = 2 supergravity theory, up to the first subleading order in their charges
The results obtained for the entropy of BPS black holes are highly satisfactory and have led to a deeper understanding of both black hole physics and statistical string theory, it would be much more insightful to have the equivalence between the two systems worked out in the more general context of non-BPS black holes and non-BPS stringy states
In this paper we use another, different but equivalent, method, known as the “entropy function formalism”, given by Sen [3], which is well-suited to compute the macroscopic entropy of extremal black holes, and sub-leading corrections thereof
Summary
We want to study the entropy of extremal, non-BPS black holes. The near horizon geometry of an extremal black hole in four dimensions is described by AdS2 × S2 metric, given by ds2 = v1. We will consider the consistent truncation of the full field configuration, satisfying the near-horizon symmetries and describing (non-)BPS black holes in N = 2 supergravity, presented in [8]. We note that the auxiliary real scalar D does not appear in the Lagrangian at the two derivative level, so in principle, it cannot be fixed Since it enters the nonlinear multiplet constraint, its most general consistent configuration is even after the higher derivative corrections are considered. As will become clear shortly, we will not need the near-horizon field configurations beyond the leading two derivative order, to compute the first order subleading corrections to the entropy of the (non)-BPS black hole solutions
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