Metastable Supertubes and non-extremal Black Hole Microstates

TL;DR

This work computes the Hamiltonian for two-charge supertubes in general three-charge bubbling geometries with a Gibbons-Hawking base and demonstrates the existence of metastable and stable non-supersymmetric minima. In a concrete two-center background, the authors show metastable tubes can decay to supersymmetric or non-supersymmetric vacua via brane-flux annihilation, with charge shifts balancing flux changes across intercenter cycles. These results support the idea that non-extremal black hole microstates can be realized as metastable or long-lived microstate geometries, informing fuzzball-like resolutions of the information paradox. The findings motivate further study of backreaction, ergoregions, and near-extremal deformations to assess the robustness and astrophysical relevance of these non-extremal microstates.

Abstract

We study the dynamics of supertubes in smooth bubbling geometries with three charges and three dipole charges that can describe black holes, black rings and their microstates. We find the supertube Hamiltonian in these backgrounds and show that there exist metastable supertube configurations, that can decay into supersymmetric and non-supersymmetric ones via brane-flux annihilation. We also find stable non-supersymmetric configurations. Both the metastable and the stable non-supersymmetric configuration are expected to describe microstate geometries for non-extremal black holes, and we discuss the implication of their existence for the fuzzball proposal.

Figures (9)

• Figure 1: Penrose diagrams for the extremal (left) and non-extremal (right) Reissner-Nordström black hole. There is a growing body of work supporting the idea that the extremal black hole singularity is resolved at horizon scale. For non-extremal black holes it is unclear whether the singularity resolution extends to the inner horizon, or all the way to the outer horizon, as in Mathur's proposal.
• Figure 2: A smooth three-charge bubbling geometry with a supertube (red) placed on one of the cycles along $\psi$.
• Figure 3: A single stable minimum between the two centers. When both charges are positive and have the same orientation as the background (which has electric potential $Z >0$ at the left center), the minimum is supersymmetric. When one of the charges has the wrong orientation, the minimum is non-supersymmetric. Note that the apparent second minimum outside the 2-center range is connected to the one inside by a Mexican-hat-type potential around the center in the $z-\rho$ plane. As we will show below in fig. \ref{['fig:Mexican_Hat']}, when supersymmetry is broken this Mexican-hat potential is slightly tilted.
• Figure 4: When one of the effective charges is zero, the supertube degenerates. In this example, we choose $Q_2 + \frac{K}{V}|_{r_1} = 0$. (Remember we work in patch "1" where $\frac{K}{V}|_{r_1}=0$.) When the other charge has the same orientation as the background, the minimum is supersymmetric (a), when the orientations are opposite, the minimum is non-supersymmetric (b).
• Figure 5: Two supersymmetric minima between the centers. When $Q_2 = 0$ in patch "1", the minimum close to the left center degenerates, and the supertube becomes a collection of parallel branes. Again, the additional minima outside the 2-center range are connected to the ones inside by a Mexican-hat-type potential around the respective center in the $z-\rho$ plane.