Abstract
Abstract We embed the general solution for non-BPS extremal asymptotically flat static and under-rotating black holes in abelian gauged D = 4 $ \mathcal{N}=2 $ supergravity, in the limit where the scalar potential vanishes but the gauging does not. Using this result, we show explicitly that some supersymmetries are preserved in the near horizon region of all the asymptotically flat solutions above, in the gauged theory. This reveals a deep relation between microscopic entropy counting of extremal black holes in Minkowski and BPS black holes in AdS. Finally, we discuss the relevance of this construction to the structure of asymptotically AdS4 black holes, as well as the possibility of including hypermultiplets.
Highlights
We show that the attractor geometries, and the microscopic counting, for BPS black holes in AdS4 [28,29,30, 35] and asymptotically flat extremal non- BPS black holes [36,37,38,39,40,41] fall within a common class of supersymmetric AdS2×S2 spaces,1 or their rotating generalizations
We conclude that the near horizon region of static asymptotically flat extremal black holes can be viewed as a special case of the general attractor geometry for BPS black holes in abelian gauged supergravity, upon restricting the FI parameters to be a very small vector, leading to a flat potential
We further showed explicitly that the attractor geometries of these black holes belong to the generic class of 1/2-BPS AdS2×S2 attractor backgrounds that pertain to black holes in abelian gauged theories
Summary
We present the essential argument of the ungauging procedure for black hole solutions and provide an explicit example by considering the static case for simplicity. We employ covariant notation when dealing with the bosonic sector and covariantise the fermionic supersymmetry variations (see section 3), so that we do not have to choose a frame for the FI terms explicitly Given these definitions, we discuss the connection of the gauged action above to the ungauged theory, at the bosonic level. (2.6) is an example solution for any cubic model, symmetric or not, and one may construct more general examples by acting with dualities.5 Given this special situation, it is natural to consider the possibility of finding asymptotically flat backgrounds in a gauged theory with a flat gauging as above. A vector of parameters in a doubly critical orbit was recently encountered in [20, 52, 53], which considered the general under-rotating extremal black hole solutions in ungauged extended supergravity. The presence of such a vector in asymptotically flat solutions can be seen to arise naturally by viewing the ungauged theory as a gauged theory with G ∈ S, leading to an interpretation of the auxiliary parameters introduced in [20, 52, 53] as residual FI terms
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