Three-charge Black Holes Research Articles

New superstrata from three-dimensional supergravity

We find a two-parameter family of generalized superstrata that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to SO(3). We also confirm that the other known families of microstrata are not supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

BPS equations and non-trivial compactifications

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, mathcal{Y} , as opposed to simply a T6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact “local model” and take the compactification manifold to be mathcal{Y}={mathrm{mathcal{M}}}_{mathrm{GH}}times {T}^2 , where ℳGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on mathcal{Y} . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of mathcal{Y} depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

One thousand and one bubbles

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.

A systematic construction of microstate geometries with low angular momentum

We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corre-sponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata [1], and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular mo-mentum [2]. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology.

Three-charge black holes and quarter BPS states in Little String Theory

We show that the system of $k$ NS5-branes wrapping $\mathbb{T}^4\times S^1$ has non-trivial vacuum structure. Different vacua have different spectra of 1/4 BPS states that carry momentum and winding around the $S^1$. In one vacuum, such states are described by black holes; in another, they can be thought of as perturbative BPS states in Double Scaled Little String Theory. In general, both kinds of states are present. We compute the degeneracy of perturbative BPS states exactly, and show that it differs from that of the corresponding black holes. We comment on the implication of our results to the black hole microstate program, UV/IR mixing in Little String Theory, string thermodynamics, the string/black hole transition, and other issues.

Habemus superstratum! A constructive proof of the existence of superstrata

We construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T^4 or K3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary function of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.

On the oscillation of species

We describe a new class of BPS objects called magnetubes: their supersymmetry is determined by their magnetic charges, while their electric charges can oscillate freely between different species. We show how to incorporate these objects into microstate geometries and create BPS solutions in which the charge densities rotate through different U(1) species as one moves around a circle within the microstate geometry. Our solutions have the same "time-like" supersymmetry as five-dimensional, three-charge black holes but, in various parts of the solution, the supersymmetry takes the "null" form that is normally associated with magnetic charges. It is this property that enables the species oscillation of magnetubes to be compatible with supersymmetry. We give an example in which the species oscillate non-trivially around a circle within a microstate geometry, and yet the energy-momentum tensor and metric are completely independent of this circle: only the amplitude of the oscillation influences the metric.

New instability of non-extremal black holes: spitting out supertubes

Abstract We search for stable bound states of non-extremal rotating three-charge black holes in five dimensions (Cvetic-Youm black holes) and supertubes. We do this by studying the potential of supertube probes in the non-extremal black hole background and find that generically the marginally bound state of the supersymmetric limit becomes metastable and disappears with non-extremality (higher temperature). However near extremality there is a range of parameters allowing for stable bound states, which have lower energy than the supertube-black hole merger. Angular momentum is crucial for this effect. We use this setup in the D1-D5 decoupling limit to map a thermodynamic instability of the CFT (a new phase which is entropically dominant over the black hole phase) to a tunnelinginstability of the black hole towards the supertube-black hole bound state. This generalizes the results of [1], which mapped an entropy enigma in the bulk to the dual CFT in a supersymmetric setup.

Calculating the jet-quenching parameter in STU background

In this paper we use the AdS/CFT correspondence to compute the jet-quenching parameter in a N=2 thermal plasma. We consider the general three-charge black hole and discuss some special cases. We add a constant electric field to the background and find the effect of the electric field on the jet-quenching parameter. Also we include higher derivative terms and obtain the first-order correction for the jet-quenching parameter.

Multi-center non-BPS black holes — the solution

We construct multi-center, non-supersymmetric four-dimensional solutions describing a rotating black hole and an arbitrary number of D4-D2-D0 black holes in a line. These solutions correspond to an arbitrary number of extremal non-BPS black rings in a Taub-NUT space with a rotating three-charge black hole in the middle. The positions of the centers are determined by solving a set of ``bubble'' or ``integrability'' equations that contain cubic polynomials of the inter-center distance, and that allow scaling solutions even when the total four-dimensional angular momentum of the scaling centers is non-zero.

Supertubes in bubbling backgrounds: Born-Infeld meets supergravity

We discuss two ways in which one can study two-charge supertubes as components of generic three-charge, three-dipole charge supergravity solutions. The first is using the Born-Infeld action of the supertubes, and the second is via the complete supergravity solution. Even though the Born-Infeld description is only a probe approximation, we find that it gives exactly the same essential physics as the complete supergravity solution. Since supertubes can depend on arbitrary functions, our analysis strengthens the evidence for the existence of three-charge black-hole microstate geometries that depend on an infinite set of parameters, and sets the stage for the computation of the entropy of these backgrounds. We examine numerous other aspects of supertubes in three-charge, three-dipole charge supergravity backgrounds, including chronology protection during mergers, the contribution of supertubes to the charges and angular momenta, and the enhancement of their entropy. In particular, we find that entropy enhancement affects supertube fluctuations both along the internal and the spacetime directions, and we prove that the charges that give the enhanced entropy can be much larger than the asymptotic charges of the solution. We also re-examine the embedding of five-dimensional black rings in Taub-NUT, and show that in different coordinate patches a ring can correspond to different four-dimensional black holes. Last, but not least, we show that all the three-charge black hole microstate geometries constructed so far can be embedded in AdS_3 x S^3, and hence can be related to states of the D1-D5 CFT.

Foaming three-charge black holes

We find a very large set of smooth horizonless geometries that have the same charges and angular momenta as the five-dimensional, maximally spinning, three-charge, supersymmetric black hole (${J}^{2}={Q}^{3}$). Our solutions are constructed using a four-dimensional Gibbons-Hawking base space that has a very large number of two-cycles. The entropy of our solutions is proportional to $\sqrt{Q}$. In the same class of solutions we also find microstates corresponding to zero-entropy black rings, and these are related to the microstates of the black hole by continuous deformations.

Three-charge black holes on a circle

We study phases of five-dimensional three-charge black holes with a circle in their transverse space. In particular, when the black hole is localized on the circle we compute the corrections to the metric and corresponding thermodynamics in the limit of small mass. When taking the near-extremal limit, this gives the corrections to the constant entropy of the extremal three-charge black hole as a function of the energy above extremality. For the partial extremal limit with two charges sent to infinity and one finite we show that the first correction to the entropy is in agreement with the microscopic entropy by taking into account that the number of branes shift as a consequence of the interactions across the transverse circle. Beyond these analytical results, we also numerically obtain the entire phase of non- and near-extremal three- and two-charge black holes localized on a circle. More generally, we find in this paper a rich phase structure, including a new phase of three-charge black holes that are non-uniformly distributed on the circle. All these three-charge black hole phases are found via a map that relates them to the phases of five-dimensional neutral Kaluza-Klein black holes.

Mergers and typical black hole microstates

We use mergers of microstates to obtain the first smooth horizonless microstate solutions corresponding to a BPS three-charge black hole with a classically large horizon area. These microstates have very long throats, that become infinite in the classical limit; nevertheless, their curvature is everywhere small. Having a classically-infinite throat makes these microstates very similar to the typical microstates of this black hole. A rough CFT analysis confirms this intuition, and indicates a possible class of dual CFT microstates. We also analyze the properties and the merging of microstates corresponding to zero-entropy BPS black holes and black rings. We find that these solutions have the same size as the horizon size of their classical counterparts, and we examine the changes of internal structure of these microstates during mergers.

Thermodynamics of R-charged Black Holes inAdS5×S5from Effective Strings

It is well known that the thermodynamics of certain near-extremal black holes in asymptotically flat space can be lifted to an effective string description created from the intersection of D-branes. In this paper we present evidence that the semiclassical thermodynamics of near-extremal R-charged black holes in AdS5 × S5 is described in a similar manner by effective strings created from the intersection of giant gravitons on the S5. We also present a free fermion description of the supersymmetric limit of the one-charge black hole, and we give a crude catalog of the microstates of the two and three-charge black holes in terms of operators in the dual conformal field theory.

Splitting hairs of the three charge black hole

We construct the large radius limit of the metric of three-charge supertubes and three-charge BPS black rings by using the fact that supertubes preserve the same supersymmetries as their component branes. Our solutions reproduce a few of the properties of three-charge supertubes found recently using the Born-Infeld description. Moreover, we find that these solutions pass a number of rather nontrivial tests which they should pass if they are to describe some of the hair of three-charge black holes and three-charge black rings.

Counting supertubes

The quantum states of the supertube are counted by directly quantizing the linearized Born-Infeld action near the round tube. The result is an entropy S = 2π(2(QD0QF1−J))1/2, in accord with conjectures in the literature. As a result, supertubes may be the generic D0-F1 bound state. Our approach also shows directly that supertubes are marginal bound states with a discrete spectrum. We also discuss the relation to recent suggestions of Mathur et al involving three-charge black holes.

Instanton moduli and brane creation

We obtain new intersecting 5-brane, string and pp-wave solutions in the heterotic string on a torus and on a K3 manifold. In the former case the 5-brane is supported by Yang–Mills instantons, and in the latter case both the 5-brane and the string are supported by the instantons. The instanton moduli are parameterised by the sizes and locations of the instantons. We exhibit two kinds of phase transition in which, for suitable choices of the instanton moduli, a 5-brane and/or a string can be created. One kind of phase transition occurs when the size of an instanton vanishes, while the other occurs when a pair of Yang–Mills instantons coalesce. We also study the associated five-dimensional black holes and the implications of these phase transitions for the black-hole entropy. Specifically, we find that the entropy of the three-charge black holes is zero when the instantons are separated and of non-zero scale size, but becomes non-zero (which can be counted microscopically) after either of the phase transitions.

One ring to rule them all and in the darkness bind them?

We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R^4 transverse to the branes. The black rings copiously violate black hole uniqueness. The supertube solutions are completely regular, and generically have small curvature. They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.