arXiv subjects

Oscar J. C. Dias

Publications and source records attributed to Oscar J. C. Dias.

At least 55 records · Page 3Linked to original sources

arXiv2017

Lattice Black Branes: Sphere Packing in General Relativity

We perturbatively construct asymptotically $\mathbb{R}^{1,3}\times\mathbb{T}^2$ 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.

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arXiv2017

Collapse and Nonlinear Instability of AdS with Angular Momenta

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 timescale for collapse at low energies $E$, keeping the angular momenta $J\propto E$ in AdS length units. We find that the inclusion of angular momenta delays the collapse time, but retains a $t\sim1/E$ scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS appear stable, but those sufficiently far from AdS 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.

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arXiv2017

AdS nonlinear instability: breaking spherical and axial symmetries

Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravitational sector, where spherical symmetry is necessarily broken. In \cite{Bizon:2011gg} the onset of such nonlinear instability was associated with the existence of irremovable secular resonances at third order in perturbation theory. Furthermore, it was also conjectured in \cite{Bizon:2011gg} that certain very fine tuned initial data would not collapse. Such solutions, upon linearisation, correspond to individual normal modes of AdS, which can be consistently backreacted to all orders in perturbation theory. However, the analysis of \cite{Bizon:2011gg} was restricted to spherical symmetry. The perturbative arguments of \cite{Bizon:2011gg} were then generalised to gravitational perturbations in \cite{Dias:2011ss}, and in particular certain time-periodic solutions were also conjectured to exist - these were coined geons. However, in \cite{Dias:2011ss}, only a certain class of perturbations was considered, for which the perturbative analysis considerably simplifies. In this manuscript we present details of the systematic computational formalism and an exhaustive and complementary analysis of physical properties of the geons and gravitational AdS instability that were absent in our companion Letter \cite{Dias:2016ewl}. In particular, we find that, unlike in spherical symmetry, a (single) gravitational normal mode of AdS can be backreacted to generate a nonlinear solution only in very exceptional circumstances. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, and give evidence suggesting that the former dominates the latter for equal energy two-mode seeds.

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arXiv2017

Mass-deformed M2 branes in Stenzel space

We obtain finite-temperature M2 black branes in 11-dimensional supergravity, in a $G_4$-flux background whose self-dual part approaches a solution of Cvetič, Gibbons, Lü, and Pope, based upon Stenzel's family of Ricci-flat Kähler deformed cones. Our solutions are asymptotically $AdS_4$ times a 7-dimensional Stiefel manifold $V_{5,2}$, and the branes are ``smeared'' to retain $SO(5)$ symmetry in the internal space. The solutions represent a mass deformation of the corresponding dual $CFT_3$, whose full description is at this time only partially-understood. We investigate the possibility of a confinement/de-confinement phase transition analogous to the $AdS_5 \times S^5$ case, and a possible Gregory-Laflamme type instability which could lead to polarised brane solutions which break $SO(5)$. We discuss possible consequences for AdS/CFT and the KKLT cosmological uplift mechanism.

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arXiv2017

Hairy black holes and the endpoint of AdS$_4$ charged superradiance

We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordström black hole at the onset of superradiance. These hairy black holes have, for a given mass and charge, higher entropy than the corresponding AdS$_4$-Reissner-Nordström black hole. Therefore, they are natural candidates for the endpoint of the charged superradiant instability. On the other hand, hairy black holes never dominate the canonical and grand-canonical ensembles. The zero-horizon radius of the hairy black holes is a soliton (i.e. a boson star under a gauge transformation). We construct our solutions perturbatively, for small mass and charge, so that the properties of hairy black holes can be used to testify and compare with the endpoint of initial value simulations. We further discuss the near-horizon scalar condensation instability which is also present in global AdS$_4$-Reissner-Nordström black holes. We highlight the different nature of the near-horizon and superradiant instabilities and that hairy black holes ultimately exist because of the non-linear instability of AdS.

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arXiv2017

Localised and nonuniform thermal states of super-Yang-Mills on a circle

At low energies or temperatures, maximally supersymmetric Yang-Mills theory on $\mathbb R^{(t)}\times S^1$ 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.

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arXiv2016

Localised $\bf{AdS_5\times S^5}$ Black Holes

We numerically construct asymptotically global $\mathrm{AdS}_5\times \mathrm{S}^5$ black holes that are localised on the $\mathrm{S}^5$. These are solutions to type IIB supergravity with $\mathrm S^8$ horizon topology that dominate the theory in the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to $\mathrm{AdS}_5$-Schwarzschild$\times \mathrm{S}^5$. By the AdS/CFT correspondence, this transition is dual to spontaneously breaking the $SO(6)$ R-symmetry of $\mathcal N=4$ super Yang-Mills down to $SO(5)$. We extrapolate the location of this phase transition and compute the expectation value of the resulting scalar operators in the low energy phase.

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arXiv2016

AdS nonlinear instability: moving beyond spherical symmetry

Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.

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arXiv2015

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$_5\times S^5$. We also include several tools and tricks that have been useful throughout the literature.

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arXiv2015

Black holes with a single Killing vector field: black resonators

We 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.

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arXiv2015

Lumpy AdS$\bf{_5\times}$ S$\bf{^5}$ Black Holes and Black Belts

Sufficiently small Schwarzschild black holes in global AdS$_5\times$S$^5$ 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 S$^5$ down to SO$(5)$. These new "lumpy" solutions are labelled by the harmonics $\ell$. We find evidence that the $\ell = 1$ branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S$^8$ topology. We argue that these S$^8$ 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 $\ell = 2$. 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 $\mathrm S^4\times\mathrm S^4$ which we call a "black belt".

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arXiv2015

Linear mode stability of Kerr-Newman and its quasinormal modes

We provide strong evidence that, up to $99.999\%$ of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant fields that describe the most general linear perturbations of a KN BH (except for trivial modes that shift the parameters of the solution). We determine the quasinormal mode (QNM) spectrum of the KN BH as a function of its three parameters and find no unstable modes. In addition, we find that the QNMs that are connected continuously to the gravitational $\ell=m=2$ Schwarzschild QNM dominate the spectrum for all values of the parameter space ($m$ is the azimuthal number of the wave function and $\ell$ measures the number of nodes along the polar direction). Furthermore, all QNMs with $\ell=m$ approach Re$\,ω= m Ω_H^{ext}$ and Im$\,ω=0$ at extremality; this is a universal property for any field of arbitrary spin $|s|\leq 2$ propagating on a KN BH background ($ω$ is the wave frequency and $Ω_H^{ext}$ the BH angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement. We also present a simple proof that the Regge-Wheeler (odd) and Zerilli (even) sectors of Schwarzschild perturbations must be isospectral.

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arXiv2014

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.

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arXiv2014

Quasinormal modes of asymptotically flat rotating black holes

We study the main properties of general linear perturbations of rotating black holes in asymptotically flat higher-dimensional spacetimes. In particular, we determine the quasinormal mode (QNM) spectrum of singly spinning and equal angular momenta Myers-Perry black holes (MP BHs). Emphasis is also given to the timescale of the ultraspinning and bar-mode instabilities in these two families of MP BHs. For the bar-mode instabilities in the singly spinning MP BH, we find excellent agreement with our linear analysis and the non-linear time evolution of Shibata and Yoshino for d=6,7 spacetime dimensions. We find that d=5 singly spinning BHs are linearly stable. In the context of studying general relativity in the large dimension limit, we obtain the QNM spectrum of Schwarzschild BHs and rotating MP BHs for large dimensions. We identify two classes of modes. For large dimensions, we find that in the limit of zero rotation, unstable modes of the MP BHs connect to a class of Schwarzschild QNMs that saturate to finite values.

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arXiv2014

Vortices in holographic superfluids and superconductors as conformal defects

We present a detailed study of a single vortex in a holographic symmetry breaking phase. At low energies the system flows to an nontrivial conformal fixed point. Novel vortex physics arises from the interaction of these gapless degrees of freedom with the vortex: at low energies the vortex may be understood as a conformal defect in this low energy theory. Defect conformal symmetry allows the construction of a simple infrared geometry describing a new kind of extremal horizon: a Poincare horizon with a small bubble of magnetic Reissner-Nordstrom horizon inside it that carries a single unit of magnetic flux and a finite amount of entropy even at zero temperature. We also construct the full geometry describing the vortex at finite temperature in a UV complete theory. We study both superfluid and superconducting boundary conditions and calculate thermodynamic properties of the vortex. A study of vortex stability reveals that the dual superconductor can be Type I or Type II, depending on the charge of the condensed scalar. Finally, we study forces on a moving vortex at finite temperature from the point of view of defect conformal symmetry and show that these forces can be expressed in terms of Kubo formulas of defect CFT operators.

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arXiv2013

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.

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arXiv2013

Algebraically special perturbations of the Schwarzschild solution in higher dimensions

We study algebraically special perturbations of a generalized Schwarzschild solution in any number of dimensions. There are two motivations. First, to learn whether there exist interesting higher-dimensional algebraically special solutions beyond the known ones. Second, algebraically special perturbations present an obstruction to the unique reconstruction of general metric perturbations from gauge-invariant variables analogous to the Teukolsky scalars and it is desirable to know the extent of this non-uniqueness. In four dimensions, our results generalize those of Couch and Newman, who found infinite families of time-dependent algebraically special perturbations. In higher dimensions, we find that the only regular algebraically special perturbations are those corresponding to deformations within the Myers-Perry family. Our results are relevant for several inequivalent definitions of "algebraically special".

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arXiv2013

Boundary Conditions for Kerr-AdS Perturbations

The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.

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