Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras

In this paper we show that the supergravity equations describing both cosmic billiards and a large class of black-holes are, generically, both Liouville integrable as a consequence of the same universal mechanism. This latter is provided by the Liouville integrable Poissonian structure existing on the dual Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive the explicit integration algorithm associated with all symmetric spaces U/H^{*} relevant to the description of time-like and space-like p-branes. The most important consequence of our approach is the explicit construction of a complete set of conserved involutive hamiltonians h_{\alpha} that are responsible for integrability and provide a new tool to classify flows and orbits. We believe that these will prove a very important new tool in the analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two 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

Lifshitz spacetimes from AdS null and cosmological solutions

We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction of these solutions. The dual field theory in this case is a deformation of the N=4 super Yang-Mills theory. We discuss the holographic 2-point function of operators dual to bulk scalars. We further describe time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensional supergravity, which are somewhat similar to the solutions above. In some cases here, we expect the field theory duals to be deformations of the Chern-Simons theories on M2-branes stacked at singularities.Comment: Latex, 29pgs, v3. references, minor clarifications (subsection on Lifshitz geometry seen by scalar probes) added, to appear in JHE

Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

An electrically charged doubly spinning dipole black ring

We present a new asymptotically flat, doubly spinning black ring of D = 5 Einstein-Maxwell-dilaton theory with Kaluza-Klein dilaton coupling. Besides the mass and two angular momenta, the solution displays both electric charge and (magnetic) dipole charge. The class of solutions that are free from conical singularities is described by four parameters. We first derive the solution in six dimensions employing the inverse scattering method, thereby generalising the inverse-scattering construction by two of the current authors of Emparan's singly spinning dipole black ring. The novel black ring itself arises upon circle Kaluza-Klein reduction. We also compute the main physical properties and asymptotic charges of our new class of solutions. Finally, we present a five-parameter generalisation of our solution.Comment: v2: Improved presentation with new additions including plots of some physical charges and a new appendix with the most general five-parameter solution. Version to be published in JHE

Image informatics strategies for deciphering neuronal network connectivity

Brain function relies on an intricate network of highly dynamic neuronal connections that rewires dramatically under the impulse of various external cues and pathological conditions. Among the neuronal structures that show morphologi- cal plasticity are neurites, synapses, dendritic spines and even nuclei. This structural remodelling is directly connected with functional changes such as intercellular com- munication and the associated calcium-bursting behaviour. In vitro cultured neu- ronal networks are valuable models for studying these morpho-functional changes. Owing to the automation and standardisation of both image acquisition and image analysis, it has become possible to extract statistically relevant readout from such networks. Here, we focus on the current state-of-the-art in image informatics that enables quantitative microscopic interrogation of neuronal networks. We describe the major correlates of neuronal connectivity and present workflows for analysing them. Finally, we provide an outlook on the challenges that remain to be addressed, and discuss how imaging algorithms can be extended beyond in vitro imaging studies

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit