Black Holes, Black Rings and their Microstates

TL;DR

The paper surveys construction and analysis of three-charge microstate configurations in string theory, focusing on three-charge supertubes, Born-Infeld realizations, and BPS black-ring/black-hole solutions. It develops a linear, four-dimensional Gibbons-Hawking base framework to generate horizonless microstate geometries, including bubbling transitions and the 4D-5D connection, with detailed bubble equations ensuring regularity. It demonstrates that deep microstates—many-bubble geometries and mergers—exhibit long AdS-like throats and mass gaps that correspond to boundary CFT states with long component strings, supporting a microstate-based view of black holes and rings. The work argues for a rich, geometrical dictionary between bulk microstates and boundary states, with significant implications for the black hole information problem and potential observable signatures in gravitational wave phenomena. It further contemplates three philosophical possibilities about typical microstates in AdS/CFT, arguing for a bulk description in horizonless geometries that captures the microstate ensemble beyond the classical black hole geometry.

Abstract

In this review article we describe some of the recent progress towards the construction and analysis of three-charge configurations in string theory and supergravity. We begin by describing the Born-Infeld construction of three-charge supertubes with two dipole charges, and then discuss the general method of constructing three-charge solutions in five dimensions. We explain in detail the use of these methods to construct black rings, black holes, as well as smooth microstate geometries with black hole and black ring charges, but with no horizon. We present arguments that many of these microstate geometries are dual to boundary states that belong to the same sector of the D1-D5-P CFT as the typical states. We end with an extended discussion of the implications of this work for the physics of black holes in string theory.

Figures (10)

• Figure 1: An illustrative description of Mathur's conjecture. Most of the present research efforts go into improving the dictionary between bulk and boundary microstates (the dotted arrow), and into constructing more microstate geometries.
• Figure 2: The first two steps of the procedure to construct solutions. One first chooses an arbitrary M5 brane profile, and then sprinkles the various types of M2 branes, either on the M5 brane profile, or away from it. This gives a solution for an arbitrary superposition of black rings, supertubes and black holes.
• Figure 3: The configuration black ring with an off-set black hole on its axis. The parameter, $\alpha$, is related to the angle of approach, $\delta$, by $\alpha \equiv \cot {\rm \delta}$.
• Figure 4: This figure depicts some non-trivial cycles of the Gibbons-Hawking geometry. The behaviour of the $U(1)$ fiber is shown along curves between the sources of the potential, $V$. Here the fibers sweep out a pair of intersecting homology spheres.
• Figure 5: Geometric transitions: The branes wrap the large (blue) cycle; the flux through the Gaussian (small, red) cycle measures the brane charge. In the open-string picture the small (red) cycle has non-zero size, and the large (blue) cycle is contractible. After the geometric transition the size of the large (blue) cycle becomes zero, while the small (red) cycle becomes topologically non-trivial.