Static Black Binaries in de Sitter Space.

We construct the first four-dimensional multiple black hole solution of general relativity with a positive cosmological constant. The solution consists of two static black holes whose gravitational attraction is balanced by the cosmic expansion. These static binaries provide the first four-dimensional example of nonuniqueness in general relativity without matter.

Extremal Kerr Black Holes as Amplifiers of New Physics.

We show that extremal Kerr black holes are sensitive probes of new physics. Stringy or quantum corrections to general relativity are expected to generate higher-curvature terms in the gravitational action. We show that in the presence of these terms, asymptotically flat extremal rotating black holes have curvature singularities on their horizon. Furthermore, near-extremal black holes can have large yet finite tidal forces for infalling observers. In addition, we consider five-dimensional extremal charged black holes and show that higher-curvature terms can have a large effect on the horizon geometry.

Rotating Black Holes in Randall-Sundrum II Braneworlds.

We find rotating black hole solutions in the Randall-Sundrum II (RSII) model, by numerically solving a three-dimensional PDE problem using pseudospectral collocation methods. We compute the area and equatorial innermost stable orbits of these solutions. For large black holes compared with the AdS length scale ℓ the black hole exhibits four-dimensional behavior, approaching the Kerr metric on the brane, while for small black holes, the solution tends instead towards a five-dimensional Myers-Perry black hole with a single nonzero rotation parameter aligned with the brane. This departure from exact four-dimensional gravity may lead to different phenomenological predictions for rotating black holes in the RSII model to those in standard four-dimensional general relativity. This Letter provides a stepping stone for studying such modifications.

Charting Islands of Stability with Multioscillators in anti-de Sitter space.

We propose the existence of an infinite-parameter family of solutions in anti-de Sitter (AdS) that oscillate on any number of noncommensurate frequencies. Some of these solutions appear stable when perturbed, and we suggest that they can be used to map out the AdS "islands of stability." By numerically constructing two-frequency solutions and exploring their parameter space, we find that both collapse and noncollapse are generic scenarios near AdS. Unlike other approaches, our results are valid on any timescale and do not rely on perturbation theory.

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

Scalar Hairy Black Holes in Four Dimensions are Unstable.

We present a numerical analysis of the stability properties of the black holes with scalar hair constructed by Herdeiro and Radu. We prove the existence of a novel gauge where the scalar field perturbations decouple from the metric perturbations, and analyze the resulting quasinormal mode spectrum. We find unstable modes with characteristic growth rates which for uniformly small hair are almost identical to those of a massive scalar field on a fixed Kerr background.

Collapse and Nonlinear Instability of AdS Space with Angular Momentum.

We present a numerical study of rotational dynamics in AdS_{5} with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the time scale for collapse at low energies E, keeping the angular momenta J∝E in anti-de Sitter (AdS) length units. We find that the inclusion of angular momenta delays the collapse time, but retains a t∼1/E scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS space appear stable, but those sufficiently far from AdS space are unstable. We find that the dynamics of the boson star instability depend on the perturbation, resulting either in collapse to a Myers-Perry black hole, or development towards a stable oscillating solution.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space.

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Localized AdS_{5}×S

According to heuristic arguments, global AdS_{5}×S^{5} black holes are expected to undergo a phase transition in the microcanonical ensemble. At high energies, one expects black holes that respect the symmetries of the S^{5}; at low energies, one expects "localized" black holes that appear pointlike on the S^{5}. According to anti-de Sitter/conformal field theory correspondence, N=4 supersymmetric Yang-Mills (SYM) theory on a 3-sphere should therefore exhibit spontaneous R-symmetry breaking at strong coupling. In this Letter, we numerically construct these localized black holes. We extrapolate the location of this phase transition, and compute the expectation value of the broken scalar operator with lowest conformal dimension. Via the correspondence, these results offer quantitative predictions for N=4 SYM theory.

Neutral Black Rings in Five Dimensions are Unstable.

We study nonaxisymmetric linearized gravitational perturbations of the Emparan-Reall black ring using numerical methods. We find an unstable mode whose onset lies within the "fat" branch of the black ring and continues into the "thin" branch. Together with previous results using Penrose inequalities that fat black rings are unstable, this provides numerical evidence that the entire black ring family is unstable.

Linear mode stability of the Kerr-Newman black hole and its quasinormal modes.

We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two partial differential equations for two gauge invariant fields that describe the most general linear perturbations of a KNBH. We determine the quasinormal mode (QNM) spectrum of the KNBH as a function of its three parameters and find no unstable modes. In addition, we find that the lowest radial overtone QNMs that are connected continuously to the gravitational ℓ=m=2 Schwarzschild QNM dominate the spectrum for all values of the parameter space (m is the azimuthal number of the wave function and ℓ measures the number of nodes along the polar direction). Furthermore, the (lowest radial overtone) QNMs with ℓ=m approach Reω=mΩH(ext) and Imω=0 at extremality; this is a universal property for any field of arbitrary spin |s|≤2 propagating on a KNBH background (ω is the wave frequency and ΩH(ext) the black hole angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement.

Disordered horizons: holography of randomly disordered fixed points.

We deform conformal field theories with classical gravity duals by marginally relevant random disorder. We show that the disorder generates a flow to IR fixed points with a finite amount of disorder. The randomly disordered fixed points are characterized by a dynamical critical exponent z > 1 that we obtain both analytically (via resummed perturbation theory) and numerically (via a full simulation of the disorder). The IR dynamical critical exponent increases with the magnitude of disorder, probably tending to z → ∞ in the limit of infinite disorder.

Holographic Josephson junctions.

We construct a gravitational dual of a Josephson junction. Calculations on the gravity side reproduce the standard relation between the current across the junction and the phase difference of the condensate. We also study the dependence of the maximum current on the temperature and size of the junction and reproduce familiar results.