A (Running) Bolt for New Reasons

TL;DR

The paper constructs explicit non-BPS, horizonless five-dimensional geometries—running Bolt and running Taub-Bolt—by magnetizing Euclidean Schwarzschild and Kerr-Taub-Bolt bases within ungauged STU-like supergravity. These solutions share the same charges and mass as corresponding non-extremal black holes and exhibit a mixed time/Kaluza-Klein fiber at infinity; the base can be ambi-polar, enlarging the allowed parameter space and yielding multiple branches. A key finding is that the rest mass can either increase or decrease with added M2 charge, depending on the self-duality of the flux, with anti-self-dual cases even lowering mass without violating energy conservation due to the non-supersymmetric setting. The results provide concrete horizonless microstate geometries that support a fuzzball-like resolution of spacelike singularities for non-extremal black holes and point toward avenues for constructing large multi-bubble non-extremal configurations.

Abstract

We construct a four-parameter family of smooth, horizonless, stationary solutions of ungauged five-dimensional supergravity by using the four-dimensional Euclidean Schwarzschild metric as a base space and "magnetizing" its bolt. We then generalize this to a five-parameter family based upon the Euclidean Kerr-Taub-Bolt. These "running Bolt" solutions are necessarily non-static. They also have the same charges and mass as a non-extremal black hole with a classically-large horizon area. Moreover, in a certain regime their mass can decrease as their charges increase. The existence of these solutions supports the idea that the singularities of non-extremal black holes are resolved by low-mass modes that correct the singularity of the classical black hole solution on large (horizon-sized) scales.

Figures (3)

• Figure 1: Plot of the scale, $\sqrt{{\cal M} }$, of the compactification circle as a function of $r/m$. The three plots, from top to bottom, correspond to $q/m$ of $1/4$, $1/2$ and $3/4$. Note that as one approaches the upper bound (\ref{['chcond1']}) the circle does not grow uniformly but attains a maximum scale before decreasing asymptotically.
• Figure 2: The three graphs are plots of $m$ versus $\alpha$, in units in which $N=1$ (this choice can always be made because the equations are homogeneous). The first shows the regions where $P_{r+}$ is either positive (R1, in white) or negative (R2, in green). The grey area, No, is forbidden by the reality condition, (\ref{['rplusreal']}). The second and the third graph show the solutions of (\ref{['cubic1']}) and (\ref{['cubic2']}). In the shaded (blue) areas the square root in equation (\ref{['paramreln']}) is equal to a negative expression. Hence, the solutions that belong to these regions, or to the regions of the first graph where $P_{r+}$ has the wrong sign, do not obey (\ref{['paramreln']}) and are "wrong branch" solutions. These solutions are represented using dotted lines, while the physical solutions, that obey (\ref{['paramreln']}), are represented using continuous lines and belong to the white areas.
• Figure 3: Plot of the values of $m$ that give physical solutions of (\ref{['paramreln']}) for a given $\alpha$, in units in which $N=1$. The solution has four disconnected branches: Branches I ,II and III go from $\alpha=0$ to $\alpha=1$, diverging as $\alpha$ approaches 1. Branch IV starts from $-\infty$ as $\alpha \rightarrow 1_+$ and approaches $m=2$ as $\alpha \rightarrow \infty$. The intercepts, C and D, correspond, respectively, to the Taub-NUT and Taub-Bolt metrics.