Supergravity Microstates for BPS Black Holes and Black Rings

TL;DR

This work constructs horizonless microstate geometries for five-dimensional, 3-charge BPS black holes and black rings in the D1/D5/P system by extending the Bena–Warner framework to include a time fibration over a (potentially singular) hyper-Kähler base. The solution is encoded in eight harmonic functions on $\mathbb{R}^3$, with an arbitrary arrangement of positive and negative poles in the base function $H$, enabling a geometric transition where singular sources are replaced by flux through two-cycles, and preserving asymptotic charges. The authors derive explicit expressions for the warp factors $Z_i$, the angular-momentum one-form $k$, and the flux data, along with stringent smoothness, causality, and topology constraints, which ensure absence of horizons and closed timelike curves and enumerate the flux quantization on internal cycles. A two-pole example demonstrates the feasibility of the construction and illustrates how microstate geometries can realize black hole-like charges while remaining horizonless, highlighting the potential to generate a broad class of microstates for 5D black objects. This approach offers a concrete, U(1)-invariant path toward cataloging black hole microstates within string theory and deepening our understanding of black hole information in holographic contexts.

Abstract

We demonstrate a solution generating technique, modulo some constraints, for a large class of smooth supergravity solutions with the same asymptotic charges as a five dimensional 3-charge BPS black hole or black ring, dual to a D1/D5/P system. These solutions are characterized by a harmonic function with both positive and negative poles, which induces a geometric transition whereby singular sources have disappeared and all of the net charge at infinity is sourced by fluxes through two-cycles joining the poles of the harmonic function.

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