The Nuts and Bolts of Einstein-Maxwell Solutions

TL;DR

The paper constructs explicit, non-supersymmetric, horizonless solutions in five-dimensional $\mathcal{N}=2$ ungauged supergravity coupled to two vector multiplets by leveraging a four-dimensional electrovac base and a floating-brane linear system. Starting from a Euclidean dyonic Reissner–Nordström base and then incorporating rotation and NUT charge to obtain a Kerr–Newman–NUT base, the authors solve a cascade of linear equations to determine the warp factors, fluxes, and angular momentum, yielding regular geometries with the same asymptotics as non-extremal black holes. The solutions admit an uplift to eleven-dimensional supergravity on $T^6$ and can be interpreted in terms of M2/M5 brane fluxes dissolved in the base topology, with the mass remaining linear in the charges due to the floating-brane Ansatz. A notable feature is ambipolarity: the four-dimensional base may change signature while the five-dimensional solution stays regular and causal, illustrating a broad class of non-BPS microstate geometries for non-extremal black holes. The work suggests further generalizations via Calabi–Yau compactifications and spectral-flow techniques, and raises questions about stability and holographic interpretations for these non-supersymmetric microstate geometries.

Abstract

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An essential ingredient in our construction is a four-dimensional Euclidean base which is a solution to Einstein-Maxwell equations. We construct stationary solutions based on the Euclidean dyonic Reissner-Nordstrom black hole as well as a six-parameter family with a dyonic Kerr-Newman-NUT base. These solutions can be viewed as compactifications of eleven-dimensional supergravity on a six-torus and we discuss their brane interpretation.

Figures (2)

• Figure 1: $\mathcal{M}$ as a function of $\rho=r/r_{+}$ for four different values of $Q/m$. The curves correspond to $Q/m=(0.1,0.2,0.3,0.4)$ from top to bottom.
• Figure 2: The two graphs represented here are plots of $m$ as a function of $\alpha$, in units in which $N=1$ (this choice can always be made because the equations are homogeneous). They show the solutions to \ref{['paramrelation']} for $p^2-q^2=2$ (left) and $p^2-q^2=-3/4$ (right). As the value of $p^2-q^2$ changes, the different branches of the solution evolve and some non trivial differences can be seen. For example, for $p^2-q^2=2$, one can see that there is only one possible value of $m$ for $\alpha=0$, in contrast with the three different possibilities for $p^2-q^2=-3/4$. The important feature is that for any given value of $p^2-q^2$, there will always be a solution to \ref{['paramrelation']}.