Static BPS Black Holes in AdS4 with General Dyonic Charges

TL;DR

The paper solves the general static BPS AdS$_4$ black hole problem in ${\cal N}=2$ FI-gauged supergravity with homogeneous very special Kähler scalars, showing the horizon geometry and entropy are controlled by the quartic invariant $I_4$. By introducing a warp-factor ansatz $e^V = r\sqrt{v_4 r^2 + v_3 r + v_2}$ and an ansatz for $\mathrm{Im}\,\widetilde{\cal V}$, the authors obtain closed-form expressions for the BPS solution in terms of $I_4$ and its derivative $I'_4$, parameterized by $2n_v$ independent charges subject to two algebraic constraints. A novel feature is a non-constant phase $\psi$ of the supersymmetry parameter across the spacetime, with the horizon corresponding to a double root of a quartic polynomial in the radial coordinate. In the STU model, these solutions uplift to M-theory as wrapped M2-branes with internal angular momentum, providing a holographic and geometric link to BPS AdS$_4$ black holes and suggesting avenues for extending to hypermultiplet sectors.

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 homogeneous very special Kahler 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 $AdS_2\times Σ_g$. 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.