Pair creation of particles and black holes in external fields

It is well known that massive black holes may form through the gravitational collapse of a massive astrophysical body. Less known is the fact that a black hole can be produced by the quantum process of pair creation in external fields. These black holes may have a mass much lower than their astrophysical counterparts. This mass can be of the order of Planck mass so that quantum effects may be important. This pair creation process can be investigated semiclassically using non-perturbative instanton methods, thus it may be used as a theoretical laboratory to obtain clues for a quantum gravity theory. In this work, we review briefly the history of pair creation of particles and black holes in external fields. In order to present some features of the euclidean instanton method which is used to calculate pair creation rates, we study a simple model of a scalar field and propose an effective one-loop action for a two-dimensional soliton pair creation problem. This action is built from the soliton field itself and the soliton charge is no longer treated as a topological charge but as a Noether charge. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions greater than 2.Comment: LaTeX file (World Scientific macros), no figures, 9 pages, talk given at Xth Portuguese Meeting on Astronomy and Astrophysics, (Lisbon, Portugal, 27-28 July 2000), to be published in Proc. Xth A & A meeting, edited by J. P. S. Lemos, A. Mourao, L. Teodoro, R. Ugoccioni, (World Scientific, 2001

Hairy black holes and the endpoint of AdS4_4 charged superradiance

We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordstr\"om 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-Nordstr\"om 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-Nordstr\"om 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.Comment: 41 pages, 6 figures. v2: Minor changes to match published versio

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.Comment: 33 pages, 6 figure

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".Comment: 23 pages, no figures. v2: references added; discussion improved; matches published versio

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.Comment: 7 pages, no figures, 2 table

The return of the membrane paradigm? Black holes and strings in the water tap

Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand gravity and dynamics of black objects in higher dimensions. We provide evidence that (i) the gravitational Gregory-Laflamme instability has a classical counterpart in the Rayleigh-Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black strings break in much the same way as water from a faucet breaks up into small droplets. (ii) General rotating black holes can also be understood with this analogy. In particular, instability and bifurcation diagrams for black objects can easily be inferred. This correspondence can and should be used as a guiding tool to understand and explore physics of gravity in higher dimensions.Comment: This essay received an honorable mention in the Gravity Research Foundation Essay Competition, 2007. v2: Published versio

False vacuum decay: effective one-loop action for pair creation of domain walls

An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton-antisoliton pair production rate is calculated and one recovers Stone's exponential factor and the prefactor of Kiselev, Selivanov and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions greater than 2.Comment: 12 pages, Late

Localised AdS5×S5\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.Comment: 11 pages, 6 figure

Lumpy AdS5×\bf{_5\times} S5\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".Comment: 20 pages (plus 17 pages for Appendix on Kaluza-Klein Holography), 14 figure