Static BPS black holes in AdS4 with general dyonic charges

Abstract

We complete the study of static BPS, asymptotically AdS 4 black holes within N = 2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kähler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2n v independent parameters; there are two algebraic constraints on 2n v + 2 charges, matching our previous analysis on BPS solutions of the form AdS 2 × Σ g . As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS 4 black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.

On the on-shell: the action of AdS4 black holes

“…Starting from [3], the solution for BPS black holes in AdS 4 has been developed [19][20][21][22] and in [7] a general solution for dyonically charged, AdS 4 black holes in FI-gauged supergravity (with general dyonic gaugings) was derived. This solution assumes that M v is a homogeneous space and is presented in terms of the quartic invariant 7 I 4 .…”

“…We will not use this explicit solution in much detail but note that e 2V is a quartic polynomial. In the solution of [3] this quartic has a pair of double roots, while for the more general solutions of [7] it has a single double root (required for all zero-temperature solutions).…”

“…A third U(1) symmetry was identified which generates a third electric charge but this is equivalent to the extra (discrete) parameter obtained by enforcing (2.21) instead of (2.16). The general BPS solution was found in [7] and this solution space is six dimensional, it satisfies (2.16) and (2.20) but one can increase the solution space to seven dimensions by enforcing (2.21) at the expense of (2.16). Finally we mention [30] where a solution was found for all eight charges although the subset of these solutions which preserve supersymmetry have not yet been identified.…”

“…Finally we mention [30] where a solution was found for all eight charges although the subset of these solutions which preserve supersymmetry have not yet been identified. In the absence of scalar hair (which is not at all clear) it is reasonable to expect that the solutions of [7] are co-dimension one inside those of [30] but given the rather unwieldy nature of all these solutions, it seems challenging to make this precise.…”

“…For all the BPS solutions of [7] the metric function e 2V is a quartic polynomial and by comparison with [30] it appears that the corresponding space of finite temperature solutions has e 2V → e 2V − 2ηr (2.33)…”