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

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

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

Lumpy AdS5_{5}× S5^{5} black holes and black belts

Abstract: Sufficiently small Schwarzschild black holes in global AdS$_{5}$× 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 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 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 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 S$^{4}$ × S$^{4}$ which we call a “black belt”

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

© 2017, The Author(s). At low energies or temperatures, maximally supersymmetric Yang-Mills theory on ℝ(t)× S1 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 S1 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

The anomalous U(1) global symmetry and flavors from an SU(5) x SU(5)′' GUT in Z12−IZ_{12-I} orbifold compactification

In string compactifications, frequently there appears the anomalous U(1) gauge symmetry which belonged to E8$\times$E8 of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale, just below $10^{18\,}$GeV, by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank anti-symmetric tensor field $B_{MN}$. Below the compactification scale, there results a global symmetry U(1)$_{\rm anom}$ whose charge $Q_{\rm anom}$ is the original gauge U(1) charge. This is the most natural global symmetry, realizing the "invisible" axion. This global symmetry U(1)$_{\rm anom}$ is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, we calculate all the low energy parameters in terms of the vacuum expectation values of the standard model singlets.Comment: 18 pages, 4 figur

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 $U(1)$ charge. We include the quasi-normal modes typically dominant during a binary black hole coalescence, $(\ell,m,n) = \{(2,2,0), (2,2,1)\}$ 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 $(3,3,0)$ 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 $\bar{q} < 0.33$ 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 $\bar{q} \gtrsim 0.5$; here we also assume that the mode amplitudes are similar to the uncharged case in creating our simulated signal. Lower values, down to $\bar{q} \sim 0.3$, 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

The first minutes in the life of a peroxisomal matrix protein

In the field of intracellular protein sorting, peroxisomes are most famous by their capacity to import oligomeric proteins. The data supporting this remarkable property are abundant and, understandably, have inspired a variety of hypothetical models on how newly synthesized (cytosolic) proteins reach the peroxisome matrix. However, there is also accumulating evidence suggesting that many peroxisomal oligomeric proteins actually arrive at the peroxisome still as monomers. In support of this idea, recent data suggest that PEX5, the shuttling receptor for peroxisomal matrix proteins, is also a chaperone/holdase, binding newly synthesized peroxisomal proteins in the cytosol and blocking their oligomerization. Here we review the data behind these two different perspectives and discuss their mechanistic implications on this protein sorting pathway. This article is part of a Special Issue entitled: Peroxisomes edited by Ralf Erdmann.This work was supported by national funds through FCT – Fundação para a Ciência e a Tecnologia/MEC-Ministério da Educação e Ciência and when applicable co-funded by FEDER funds within the partnership agreement PT2020 related with the research unit number 4293; and by the project FCOMP-01-0124-FEDER-019731 (PTDC/BIABCM/118577/2010) funded by national funds through FCT and co-funded by Fundo Europeu de Desenvolvimento Regional (FEDER) through the Operation- alCompetitiveness Programme(COMPETE).A. F.D., T.F., T.A.R. and C. P. G. were supported by FCT, Programa Operacional Potencial Humano (POPH) do Quadro de Referência Estratégico Nacional (QREN), and Fundo Social Europeu (FSE)