Supergravity Solutions from Floating Branes

TL;DR

The authors introduce a floating-brane Ansatz in five-dimensional ${\cal N}=2$ supergravity with three $U(1)$ gauge fields to generate non-BPS solutions whose warp factors and electric potentials coincide. By deriving the full equations of motion and exploiting a linear system, they show that starting from a four-dimensional Euclidean electrovac base, one can construct complete five-dimensional solutions, including a new class built on Israel-Wilson bases that describe D6–anti-D6 systems kept in equilibrium by flux. They further show that spectral flow maps these solutions to almost-BPS configurations with Gibbons-Hawking bases, establishing a bridge between different solution families and revealing a rich set of smooth horizonless geometries. The results expand the landscape of extremal non-BPS black holes and bubbling solutions, offering a tractable, linear pathway to explore non-supersymmetric microstate geometries with potential implications for the fuzzball paradigm in non-BPS contexts.

Abstract

We solve the equations of motion of five-dimensional ungauged supergravity coupled to three U(1) gauge fields using a floating-brane Ansatz in which the electric potentials are directly related to the gravitational warp factors. We find a new class of non-BPS solutions, that can be obtained linearly starting from an Euclidean four-dimensional Einstein-Maxwell base. This class - the largest known so far - reduces to the BPS and almost-BPS solutions in certain limits. We solve the equations explicitly when the base space is given by the Israel-Wilson metric, and obtain solutions describing non-BPS D6 and anti-D6 branes kept in equilibrium by flux. We also examine the action of spectral flow on solutions with an Israel-Wilson base and show that it relates these solutions to almost-BPS solutions with a Gibbons-Hawking base.

Figures (1)

• Figure 1: This diagram represents four classes of solutions that can be obtained from our solution for various values of the Israel-Wilson harmonic functions. When both $V_+$ and $V_-$ are constant, the solution describes a BPS black string in $\mathbb{R}^3\times S^1$. Turning on a $\overline{{\it{KKm}}}$ charge at the center of the space ($V_- \neq 1$) the space becomes Taub-NUT, the black ring is non-BPS and the solution belongs to the almost-BPS Ansatz. Turning on a $\it{KKm}$ charge at the location of the ring, we obtain a BPS D6-D4-D2-D0 black hole. Turning on both types of KKm charges ($V_+ \neq 1$,$V_- \neq 1$), we obtain the more general non-BPS solution constructed here: a D6-D4-D2-D0 BPS four-charge black hole in a $\overline{\mathrm{D6}}$ background.