The Black Di-Ring: An Inverse Scattering Construction

We use the inverse scattering method (ISM) to derive concentric non-supersymmetric black rings. The approach used here is fully five-dimensional, and has the modest advantage that it generalizes readily to the construction of more general axi-symmetric solutions.Comment: v3: 2 subsections added, typos fixed, more refs, journal version. v4: a transcription error in the ADM mass fixe

Toric Kahler metrics and AdS_5 in ring-like co-ordinates

Stationary, supersymmetric supergravity solutions in five dimensions have Kahler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kahler metrics provide a unified framework in which to describe both the asymptotically flat and asymptotically AdS solutions. The Darboux co-ordinates used for the local description turn out to be ''ring-like.'' We conclude with an Ansatz for studying the existence of supersymmetric black rings in AdS.Comment: A new appendix derives the explicit co-ordinate transformation between the ``ring-like'' co-ordinates and the polar co-ordinates of global AdS. Also, references adde

Inverse Scattering Construction of a Dipole Black Ring

Using the inverse scattering method in six dimensions we construct the dipole black ring of five dimensional Einstein-Maxwell-dilaton theory with dilaton coupling a = 2(2/3)^(1/2).The 5d theory can be thought of as the NS sector of low energy string theory in Einstein frame. It can also be obtained by dimensionally reducing six-dimensional vacuum gravity on a circle. Our new approach uses GL(4, R) integrability structure of the theory inherited from six-dimensional vacuum gravity. Our approach is also general enough to potentially generate dipole black objects carrying multiple rotations as well as more exotic multi-horizon configurations

Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment

We study electromagnetic test fields in the background of vacuum black rings using Killing vectors as vector potentials. We consider both spacetimes with a rotating S^1 and with a rotating S^2 and we demonstrate, in particular, that the gyromagnetic ratio of slightly charged black rings takes the value g=3 (this will in fact apply to a wider class of spacetimes). We also observe that a S^2-rotating black ring immersed in an external "aligned" magnetic field completely expels the magnetic flux in the extremal limit. Finally, we discuss the mutual alignment of principal null directions of the Maxwell 2-form and of the Weyl tensor, and the algebraic type of exact charged black rings. In contrast to spherical black holes, charged rings display new distinctive features and provide us with an explicit example of algebraically general (type G) spacetimes in higher dimensions. Appendix A contains some global results on black rings with a rotating 2-sphere. Appendix C shows that g=D-2 in any D>=4 dimensions for test electromagnetic fields generated by a time translation.Comment: 22 pages, 3 figures. v2: new appendix C finds the gyromagnetic ratio g=D-2 in any dimensions, two new references. To appear in JHE

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

Rotating black rings on Taub-NUT

In this paper, we construct new solutions describing rotating black rings on Taub-NUT using the inverse-scattering method. These are five-dimensional vacuum space-times, generalising the Emparan-Reall and extremal Pomeransky-Sen'kov black rings to a Taub-NUT background space. When reduced to four dimensions in Kaluza-Klein theory, these solutions describe (possibly rotating) electrically charged black holes in superposition with a finitely separated magnetic monopole. Various properties of these solutions are studied, from both a five- and four-dimensional perspective.Comment: 33 pages, 3 figures, LaTe

Black Rings in Taub-NUT and D0-D6 interactions

We analyze the dynamics of neutral black rings in Taub-NUT spaces and their relation to systems of D0 and D6 branes in the supergravity approximation. We employ several recent techniques, both perturbative and exact, to construct solutions in which thermal excitations of the D0-branes can be turned on or off, and the D6-brane can have $B$-fluxes turned on or off in its worldvolume. By explicit calculation of the interaction energy between the D0 and D6 branes, we can study equilibrium configurations and their stability. We find that although D0 and D6 branes (in the absence of $B$ fields, and at zero temperature) repeal each other at non-zero separation, as they get together they go over continuosly to an unstable bound state of an extremal singular Kaluza-Klein black hole. We also find that, for $B$-fields larger than a critical value, or sufficiently large thermal excitation, the D0 and D6 branes form stable bound states. The bound states with thermally excited D0 branes are black rings in Taub-NUT, and we provide an analysis of their phase diagram.Comment: 50 pages, 8 figures; v3: minor changes and references added; v4: improved figs. 7 and 8, matches with published versio

Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow

A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan-Arnol’d Hamiltonian flows and for boundaryless submanifolds

An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically flat vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.Comment: 38 pages, 13 figure

Means and covariance functions for geostatistical compositional data: an axiomatic approach

This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences on the spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability