Spinning Black Binaries in de Sitter Space.

We numerically construct stationary, rotating black binaries in general relativity with a positive cosmological constant. We consider identical black holes with either aligned or anti-aligned spins. Both cases have less entropy than the corresponding single Kerr-Schwarzschild-de Sitter black hole with the same total angular momentum and cosmological horizon entropy.

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.

Multioscillating Boson Stars.

We propose that stable boson stars generically fall within an infinite-parameter family of solutions that oscillate on any number of noncommensurate frequencies. We numerically construct two-frequency solutions and explore their parameter space. These solutions merge with the standard boson star family in the limit where the nondominating frequencies are turned off.

Holographic Signatures of Critical Collapse.

Critical phenomena in gravitational collapse exhibit the universal features of self-similarity, critical scaling, and the appearance of a naked singularity. We study critical collapse in anti-de Sitter space, focusing on holographic field theory observables. We demonstrate that the echoing period, critical exponent, and signatures of the naked singularity can all be extracted from the holographic stress tensor.

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.

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.

Localized AdS_{5}×S^{5} Black Holes.

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.

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.

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.