Multi-black Hole Research Articles

Static equilibrium of multi–black holes in expanding bubbles in five dimensions

We investigate possible configurations for vacuum multiblack holes that maintain static equilibrium in expanding bubbles. Our analysis assumes a five-dimensional Weyl metric to describe the spacetime, facilitating the derivation of solutions based on the provided rod structure. We consider a spacetime having expanding bubbles caused by one or two acceleration horizons, and show that various configurations such as two bubbles, four bubbles devoid of horizons, a black saturn, a black di-ring, a bicycling black ring (orthogonal black di-ring), and a five-dimensional black hole binary can achieve equilibrium within expanding bubbles. Specifically, we demonstrate that equilibrium requires two acceleration horizons on both sides for the bicycling ring and the five-dimensional black hole binary. However, only one acceleration horizon is necessary for achieving equilibrium in the case of the black saturn and the black di-ring. Published by the American Physical Society 2024

A Classification of Supersymmetric Kaluza–Klein Black Holes with a Single Axial Symmetry

AbstractWe extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza–Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons–Hawking type. These solutions are determined by four harmonic functions on $$\mathbb {R}^3$$ R 3 with simple poles at the centres corresponding to connected components of the horizon, and fixed points of the axial symmetry. The allowed horizon topologies are $$S^3$$ S 3 , $$S^2\times S^1$$ S 2 × S 1 , and lens space L(p, 1), and the domain of outer communication may have non-trivial topology with non-contractible 2-cycles. The classification also reveals a novel class of supersymmetric (multi-)black rings for which the supersymmetric Killing field is globally null. These solutions are determined by two harmonic functions on $$\mathbb {R}^3$$ R 3 with simple poles at centres corresponding to horizon components. We determine the subclass of Kaluza–Klein black holes that can be dimensionally reduced to obtain smooth, supersymmetric, four-dimensional multi-black holes. This gives a classification of four-dimensional asymptotically flat supersymmetric multi-black holes first described by Denef et al.

Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes

We investigate which 4-derivative extensions of Einstein-Maxwell theory admit multi-extremal black hole solutions with gravitational force balanced by Coulomb force. We obtain a set of constraints on the 4-derivative couplings by exploring various probe limits in multi-black hole systems. It turns out that these constraints are tighter than those needed to protect the mass-charge ratio of extremal black holes from higher derivative corrections. In fact, they are so strong that the Majumdar-Papapetrou multi-black solutions are unmodified by the force-free combinations of the 4-derivative couplings. Explicit examples of such 4-derivative couplings are given in 4-and 5-spacetime dimensions. Interestingly these include curvature-squared supergravity actions and the quasi-topological F4 term.

The first law for stationary axisymmetric multi-black hole systems

In the framework of Einstein-Maxwell theory, we consider collinear arrays of rotating electrically charged black holes connected by Misner-Dirac strings carrying gravimagnetic and magnetic fluxes. The first law of mechanics for these systems is derived. It involves as dynamical variables the areas, angular momenta and electric charges of the various Killing horizons — black holes and Misner strings. When the gravimagnetic fluxes all vanish, the first law reduces to a form where the dynamical variables associated with the strings are the string tensions and magnetic fluxes. This form is not generically invariant under electric-magnetic duality.

On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry

We consider the classification of supersymmetric AdS5 black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics on the base space, which in symplectic coordinates are determined by a symplectic potential. We derive the general form of the symplectic potential near any component of the horizon or axis of symmetry, which determines its singular part for any black hole solution in this class, including possible new solutions such as black lenses and multi-black holes. We find that the most general known black hole solution in this context, found by Chong, Cvetic, Lü and Pope (CCLP), is described by a remarkably simple symplectic potential. We prove that any supersymmetric and toric solution that is timelike outside a smooth horizon, with a Kähler base metric of Calabi type, must be the CCLP black hole solution or its near-horizon geometry.

Towards the construction of multi-centered black holes in AdS

We find a class of approximate perturbative solutions describing multi-centered BPS black holes in asymptotically AdS4. These black holes are moving coplanarly in a circular orbit with common radius but fixed phase differences, where the radius is characterized by a common boost velocity v. While the solutions are not complete, as they are only accurate up to mathcal{O} (M2v2), we are able to locally investigate their supersymmetric properties in four-dimensional mathcal{N} = 2 supergravity. The result indicates that, while a single BPS black hole preserves half of the supersymmetries, a configuration with two or more black holes is only 1/4 BPS. These perturbative solutions reduce in the asymptotically Minkowski limit to the multi-black hole solution of Majumdar and Papapetrou.

Charged and rotating multi-black holes in an external gravitational field

We construct analytical and regular solutions in four-dimensional General Relativity which represent multi-black hole systems immersed in external gravitational field configurations. The external field background is composed by an infinite multipolar expansion, which allows to regularise the conical singularities of an array of collinear static black holes. A stationary rotating generalisation is achieved by adding independent angular momenta and NUT parameters to each source of the binary configuration. Moreover, a charged extension of the binary black hole system at equilibrium is generated. Finally, we show that the binary Majumdar–Papapetrou solution is consistently recovered in the vanishing external field limit. All of these solutions reach an equilibrium state due to the external gravitational field only, avoiding in this way the presence of any string or strut defect.

On the Existence of Scaling Multi-Centered Black Holes

For suitable charges of the constituents, the phase space of multi-centered BPS black holes in N=2 four-dimensional supergravity famously exhibits scaling regions where the distances between the centers can be made arbitrarily small, so that the bound state becomes indistinguishable from a single-centered black hole. In this note we establish necessary conditions on the Dirac product of charges for the existence of such regions for any number of centers, generalizing the standard triangular inequalities in the three-center case. Interestingly, the same conditions are necessary for the existence of multi-centered solutions at the attractor point. We prove that similar conditions are also necessary for the existence of self-stable representations of the corresponding quiver, as suggested by the duality between the Coulomb and Higgs branches of supersymmetric quantum mechanics.

On the search for multicenter AdS black holes from M-theory

We study the effective potentials for various probe branes surrounding AdS4 black holes with massive halos in consistent truncations of M-theory on the Sasaki-Einstein7 manifolds Q111 and M111. These probes are either M2 branes extended in spacetime or “particle-like” probes such as internally wrapped M2 branes and, upon reduction to type IIA String theory, D6 branes corresponding to baryon operators in the dual Chern-Simons theory. We find both global and local minima of the potential outside the horizon, indicating the existence of stable and metastable multicenter AdS black holes in the extreme mass ratio regime, at fixed temperature and charges. For the planar case, we also find an instability towards nucleation of spacetime-filling M2 branes. With this analysis, we address some open questions on the holographic description of glassy phases of matter.

Temperature and free energy of multi-black-hole systems

In the present paper, we compute the Euclidean action of a generic system consisting of $N$ arbitrary Kerr-Newman black holes located on the symmetry axis and separated from each other by massless struts. This allows us to introduce the {\it Hawking average temperature} (HAT) $\hat T$ of the multi-black hole system via the condition of vanishing the entire set of terms involving the singular horizons due to periodic time, and the resulting formula for this temperature contains solely the surface gravities $\kappa_i$ and horizon areas $A^H_i$ of the black hole constituents. We also show that the corresponding expression for the {\it free energy} of the system defined by $\hat T$ is consistent with the first law of thermodynamics and Smarr mass relations.

Many accelerating distorted black holes

An analytical solution of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The metric can be completely regularised from any conical singularity, thanks to the presence of an external gravitational field. Therefore the multi-black hole configuration can be maintained at equilibrium without the need of strings or struts. Some notable subcases such as the accelerating distorted Schwarzschild black hole and the distorted double C-metric are explicitly presented. The Smarr law and the thermodynamics of these systems is studied. The Bonnor–Swaminarayan and the Bičák–Hoenselaers–Schmidt particle metrics are recovered, through appropriate limits, from the multi-black holes solutions.

Multi-centered black holes, scaling solutions and pure-Higgs indices from localization

The Coulomb Branch Formula conjecturally expresses the refined Witten index for N=4 Quiver Quantum Mechanics as a sum over multi-centered collinear black hole solutions, weighted by so-called `single-centered' or `pure-Higgs' indices, and suitably modified when the quiver has oriented cycles. On the other hand, localization expresses the same index as an integral over the complexified Cartan torus and auxiliary fields, which by Stokes' theorem leads to the famous Jeffrey-Kirwan residue formula. Here, by evaluating the same integral using steepest descent methods, we show the index is in fact given by a sum over deformed multi-centered collinear solutions, which encompasses both regular and scaling collinear solutions. As a result, we confirm the Coulomb Branch Formula for Abelian quivers in the presence of oriented cycles, and identify the origin of the pure-Higgs and minimal modification terms as coming from collinear scaling solutions. For cyclic Abelian quivers, we observe that part of the scaling contributions reproduce the stacky invariants for trivial stability, a mathematically well-defined notion whose physics significance had remained obscure.

All Higher-Dimensional Majumdar\u2013Papapetrou Black Holes

We prove that the only asymptotically flat spacetimes with a suitably regular event horizon, in a generalised Majumdar–Papapetrou class of solutions to higher-dimensional Einstein–Maxwell theory, are the standard multi-black holes. The proof involves a careful analysis of the near-horizon geometry and an extension of the positive mass theorem to Riemannian manifolds with conical singularities. This completes the classification of asymptotically flat, static, extreme black hole solutions in this theory.

Overcharging a multi-black-hole system and cosmic censorship

We study the generalization of the gadenken experiment of overcharging an extremal black hole proposed by Wald in the context of a multi black hole solution. In particular, we attempt to overcharge a system of two extremal black holes via test particle absorption to produce a system involving a black hole and a naked singularity. If such a process is possible, then this would be a potential violation of the cosmic censorship hypothesis. However, we find that, analogous to Wald's result for a single charged black hole, such a test particle which can expose the singularity, would not be able to enter the horizon. This provides an interesting and non-trivial example that supports the validity of the cosmic censorship hypothesis in four-dimensional general relativity.

Binary black hole systems do not interact in the Kastor-Traschen spacetime

Binary black hole merger has been detected directly by LIGO. But the detail physics of binary black hole merger has not been completely revealed due to the lack of exact solution for the corresponding spacetime. Currently only numerical solutions based on some specific coordinate for binary black hole are available. If we allow to including a cosmological constant into the Einstein equation, there is a Kastor-Traschen (KT) solution describing dynamical multi black holes. Through investigation of the related Bondi-Scahs quantities we find that the corresponding gravitational radiation and electromagnetic radiation both vanish. In addition, we have done gravitational electromagnetic analysis. All these quantitative calculations indicate that KT solution does not admit gravitational radiation nor electromagnetic radiation. Based on this finding we argue that the KT solution only describes black holes touch instead of collision.

Asymptotically flat multiblack lenses

We present an asymptotically flat and stationary multi-black lens solution with bi-axisymmetry of $U(1)\times U(1)$ as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of $L(n,1)=S^3/{\mathbb Z_n}$ as well as a sphere $S^3$. Moreover, we show that in contrast to the higher dimensional Majumdar-Papapertrou multi-black hole and multi-BMPV black hole spacetimes, the metric is smooth on each horizon even if the horizon topology is spherical.

Axisymmetric multiwormholes revisited

The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.

N = 2 SUGRA BPS Multi-center Black holes, Symplectic geometry and Freudenthal transformations

We present a detailed description of N=2 stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a systematic use of the algebraic properties of the matrix of second derivatives of the prepotential, S, which in this case is a scalar-independent matrix. The anti-involution matrix S can be understood as a Freudenthal duality x˜=Sx. We show that this duality can be generalized to “Freudenthal transformations”x→λexp⁡(θS)x=ax+bx˜ under which the horizon area, ADM mass and intercenter distances scale up leaving constant the scalars at the fixed points. In the special case λ=1, “S-rotations”, the transformations leave invariant the solution. The standard Freudenthal duality can be written as x˜=exp⁡(π2S)x. We argue that these generalized transformations leave invariant not only the quadratic prepotential theories but also the general stringy extremal quartic form Δ4, Δ4(x)=Δ4(cos⁡θx+sin⁡θx˜) and therefore its entropy at lowest order.

Double images from a single black hole

In the simulations of the multi-black holes and merging black holes a larger primary image and a secondary smaller image which looks like an eyebrow and the deformation of the shadows have been observed. However, this kind of eyebrow-like structure was considered as unique feature of multi black hole systems. In this paper, we illustrate the new result that in the case of octupole distortions of a Schwarzschild black hole the local observer sees two shadows or two images for this single black hole, i.e., also an eyebrow-like structure. Presence of two images in our case is remarkable, as we have only one black hole, however, the observer sees two dark images of this single black hole.

Ultra-high energy collisions in static space-times: single versus multi-black hole cases

We consider collision of two particles near static electrically charged extremal black holes and elucidate the conditions under which the energy in the centre of mass frame \(E_{c.m.}\) grows unbounded. For a single black hole, we generalize the results obtained earlier for the Reissner–Nordström metric, to distorted black holes. In the multi-black hole space-time, qualitatively new features appear. If the point of collision is close to at least two horizons simultaneously, unbounded \(E_{c.m.}\) are possible (i) without fine-tuning of particles’ parameters, (ii) for an arbitrary mutual orientation of two velocities. Such a combination of properties (i) and (ii) has no analogues in the single black hole case and facilitates the condition of getting unbounded \(E_{c.m.}\). Collisions in the electro-vacuum Majumdar–Papapetrou metric (several extremal black holes in equilibrium) is analyzed explicitly.