145 research outputs found
Numerical methods for finding stationary gravitational solutions
The 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 AdS. We also include several tools and tricks that have been useful throughout the literature
Rings, ripples, and rotation: Connecting black holes to black rings
Singly-spinning Myers-Perry black holes in d>5 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
Ultraspinning instability: the missing link
We study linearized perturbations of Myers-Perry black holes in d=7, with two
of the three angular momenta set to be equal, and show that instabilities
always appear before extremality. Analogous results are expected for all higher
odd d. We determine numerically the stationary perturbations that mark the
onset of instability for the modes that preserve the isometries of the
background. The onset is continuously connected between the previously studied
sectors of solutions with a single angular momentum and solutions with all
angular momenta equal. This shows that the near-extremality instabilities are
of the same nature as the ultraspinning instability of d>5 singly-spinning
solutions, for which the angular momentum is unbounded. Our results raise the
question of whether there are any extremal Myers-Perry black holes which are
stable in d>5.Comment: 19 pages. 1 figur
Recommended from our members
Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS
Black holes in anti-de Sitter (AdS) backgrounds play a pivotal role in the
gauge/gravity duality where they determine, among other things, the approach to
equilibrium of the dual field theory. We undertake a detailed analysis of
perturbed Kerr-AdS black holes in four- and five-dimensional spacetimes,
including the computation of its quasinormal modes, hydrodynamic modes and
superradiantly unstable modes. Our results shed light on the possibility of new
black hole phases with a single Killing field, possible new holographic
phenomena and phases in the presence of a rotating chemical potential, and
close a crucial gap in our understanding of linearized perturbations of black
holes in anti-de Sitter scenarios
Conformal weights in the Kerr/CFT correspondence
It has been conjectured that a near-extreme Kerr black hole is described by a
2d CFT. Previous work has shown that CFT operators dual to axisymmetric
gravitational perturbations have integer conformal weights. In this paper, we
study the analogous problem in 5d. We consider the most general near-extreme
vacuum black hole with two rotational symmetries. This includes Myers-Perry
black holes, black rings and Kaluza-Klein black holes. We find that operators
dual to gravitational (or electromagnetic or massless scalar field)
perturbations preserving both rotational symmetries have integer conformal
weights, the same for all black holes considered.Comment: 19 page
Ultraspinning instability of anti-de Sitter black holes
Myers-Perry black holes with a single spin in d>5 have been shown to be
unstable if rotating sufficiently rapidly. We extend the numerical analysis
which allowed for that result to the asymptotically AdS case. We determine
numerically the stationary perturbations that mark the onset of the
instabilities for the modes that preserve the rotational symmetries of the
background. The parameter space of solutions is thoroughly analysed, and the
onset of the instabilities is obtained as a function of the cosmological
constant. Each of these perturbations has been conjectured to represent a
bifurcation point to a new phase of stationary AdS black holes, and this is
consistent with our results.Comment: 22 pages, 7 figures. v2: Reference added. Matches published versio
Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations
We construct a template to model the post-merger phase of a binary black hole
coalescence in the presence of a remnant charge. We include the
quasi-normal modes typically dominant during a binary black hole coalescence,
and also present analytical fits for the
quasinormal mode frequencies of a Kerr-Newman black hole in terms of its spin
and charge, here also including the mode. Aside from astrophysical
electric charge, our template can accommodate extensions of the Standard Model,
such as a dark photon. Applying the model to LIGO-Virgo detections, we find
that we are unable to distinguish between the charged and uncharged hypotheses
from a purely post-merger analysis of the current events. However, restricting
the mass and spin to values compatible with the analysis of the full signal, we
obtain a 90th percentile bound on the black hole
charge-to-mass ratio, for the most favorable case of GW150914. Under similar
assumptions, by simulating a typical loud signal observed by the LIGO-Virgo
network at its design sensitivity, we assess that this model can provide a
robust measurement of the charge-to-mass ratio only for values ; here we also assume that the mode amplitudes are similar to the uncharged
case in creating our simulated signal. Lower values, down to , could instead be detected when evaluating the consistency of the
pre-merger and post-merger emission.Comment: 21 pages, 11 figures, 4 tables. Matches published versio
A scalar field condensation instability of rotating anti-de Sitter black holes
Near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable
against the condensation of an uncharged scalar field with mass close to the
Breitenlohner-Freedman bound. It is shown that a similar instability afflicts
near-extreme large rotating AdS black holes, and near-extreme hyperbolic
Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole
solutions are determined numerically. Some stability results for (possibly
charged) scalar fields in black hole backgrounds are proved. For most of the
extreme black holes we consider, these demonstrate stability if the ``effective
mass" respects the near-horizon BF bound. Small spherical
Reissner-Nordstrom-AdS black holes are an interesting exception to this result.Comment: 34 pages; 13 figure
Black ringoids: spinning balanced black objects in d >= 5 dimensions - the codimension-two case
We propose a general framework for the study of asymptotically flat black objects with k+1 equal magnitude angular momenta in d >= 5 spacetime dimensions (with 0 0 are dubbed black ringoids. Based on the nonperturbative numerical results found for several values of (n, k), we propose a general picture for the properties and the phase diagram of these solutions and the associated black holes with spherical horizon topology: n = 1 black ringoids repeat the k = 0 pattern of black rings and Myers-Perry black holes in 5 dimensions, whereas n > 1 black ringoids follow the pattern of higher dimensional black rings associated with 'pinched' black holes and Myers-Perry black holes
Thermodynamic instability of doubly spinning black objects
We investigate the thermodynamic stability of neutral black objects with (at
least) two angular momenta. We use the quasilocal formalism to compute the
grand canonical potential and show that the doubly spinning black ring is
thermodynamically unstable. We consider the thermodynamic instabilities of
ultra-spinning black objects and point out a subtle relation between the
microcanonical and grand canonical ensembles. We also find the location of the
black string/membrane phases of doubly spinning black objects.Comment: 25 pages, 7 figures v2: matches the published versio
- …