1,720,973 research outputs found
Numerical methods for finding stationary gravitational solutions
Get PDFThe wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly-spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS5 × S5. We also include several tools and tricks that have been useful throughout the literature
Localised AdS<sub>5</sub> x S<sup>5</sup> black holes
No full textAccording to heuristic arguments, global AdS5×S5 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 S5; at low energies, one expects “localized” black holes that appear pointlike on the S5. 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 theor
Spinning black binaries in de Sitter space
No full textWe 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. Our solutions establish continuous nonuniqueness in general relativity without matter. They also provide initial data for the spinning binary merger problem (when orbital angular momentum is added).</p
Black holes with a single Killing vector field: black resonators
Get PDFWe numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we show that black resonators are unstable and comment on the implications for the endpoint of the superradiant instability
Localised and nonuniform thermal states of super-Yang-Mills on a circle
Get PDFAbstract At low energies or temperatures, maximally supersymmetric Yang-Mills theory on ℝ t × S 1 with large N gauge group SU(N ) and strong t’Hooft coupling is conjectured to be dual to the low energy dynamics of a collection of D0-branes on a circle. We construct thermal states in the gravitational side of the correspondence where we find a first-order phase transition between states that are uniform on the S 1 and states that are localised on it. When compared with lattice computations that are now available, these critical values provide the first instance where a first-order phase transition is tested on both sides of gauge/gravity duality
Lattice black branes: sphere packing in general relativity
No full textWe perturbatively construct asymptotically ℝ 1 , 3× T2 black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.</p
Rings, ripples, and rotation: connecting black holes to black rings
Get PDFSingly-spinning Myers-Perry black holes in d ≥ 6 spacetime dimensions are unstable for sufficiently large angular momentum. We numerically construct (in d = 6 and d = 7) two new stationary branches of lumpy (rippled) black hole solutions which bifurcate from the onset of this ultraspinning instability. We give evidence that one of these branches connects through a topology-changing merger to black ring solutions which we also construct numerically. The other branch approaches a solution with large curvature invariants. We are also able to compare the d = 7 ring solutions with results from finite-size corrections to the blackfold approach, finding excellent agreement
Lumpy AdS5× S5 black holes and black belts
No full textSufficiently small Schwarzschild black holes in global AdS5×S5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S5 down to SO(5). These new “lumpy” solutions are labelled by the harmonics ℓ. We find evidence that the ℓ = 1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S8 topology. We argue that these S8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ = 2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S4 × S4 which we call a “black belt”
Static black binaries in de Sitter
No full textWe construct the first four-dimensional multi-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 non-uniqueness in general relativity without matter
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