Closed System of Equations on a Brane

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations obtained. We consider bulk spaces with both spacelike and timelike extra dimension, with and without the $Z_2$ symmetry of reflection relative to the brane.Comment: 11 pages, revtex. Substantially revised version to be published in PL

Higher order curvature generalisations of Bartnick-McKinnon and coloured black hole solutions in d=5d=5

We construct globally regular as well as non-abelian black hole solutions of a higher order curvature Einstein-Yang-Mills (EYM) model in $d=5$ dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO(d)$ Yang--Mills hierarchy.Comment: 13 Revtex pages, 5 PS figures; discussions extended, reference adde

Bouncing Braneworlds

We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.Comment: 9 pages, 1 figure, revtex, accepted for publication in Phys. Lett.

The Topology of the AdS/CFT/Randall-Sundrum Complementarity

The background geometries of the AdS/CFT and the Randall-Sundrum theories are locally similar, and there is strong evidence for some kind of "complementarity" between them; yet the global structures of the respective manifolds are very different. We show that this apparent problem can be understood in the context of a more complete global formulation of AdS/CFT. In this picture, the brane-world arises within the AdS/CFT geometry as the inevitable consequence of recent results on the global structure of manifolds with "infinities". We argue that the usual coordinates give a misleading picture of this global structure, much as Schwarzschild coordinates conceal the global form of Kruskal-Szekeres space.Comment: 18 pages, Discussion much expanded, several references added and correcte

Black Diamonds at Brane Junctions

We discuss the properties of black holes in brane-world scenarios where our universe is viewed as a four-dimensional sub-manifold of some higher-dimensional spacetime. We consider in detail such a model where four-dimensional spacetime lies at the junction of several domain walls in a higher dimensional anti-de Sitter spacetime. In this model there may be any number p of infinitely large extra dimensions transverse to the brane-world. We present an exact solution describing a black p-brane which will induce on the brane-world the Schwarzschild solution. This exact solution is unstable to the Gregory-Laflamme instability, whereby long-wavelength perturbations cause the extended horizon to fragment. We therefore argue that at late times a non-rotating uncharged black hole in the brane-world is described by a deformed event horizon in p+4 dimensions which will induce, to good approximation, the Schwarzschild solution in the four-dimensional brane world. When p=2, this deformed horizon resembles a black diamond and more generally for p>2, a polyhedron.Comment: 13 pages, 1 figure, latex, JHEP.cl

Strong Interactions and Stability in the DGP Model

The model of Dvali, Gabadadze, and Porrati (DGP) gives a simple geometrical setup in which gravity becomes 5-dimensional at distances larger than a length scale \lambda_{DGP}. We show that this theory has strong interactions at a length scale \lambda_3 ~ (\lambda_{DGP}^2 / M_P)^{1/3}. If \lambda_{DGP} is of order the Hubble length, then the theory loses predictivity at distances shorter than \lambda_3 ~ 1000 km. The strong interaction can be viewed as arising from a longitudinal `eaten Goldstone' mode that gets a small kinetic term only from mixing with transverse graviton polarizations, analogous to the case of massive gravity. We also present a negative-energy classical solution, which can be avoided by cutting off the theory at the same scale scale \lambda_3. Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.Comment: 24 pages, LaTeX2e, no figure

Gravitational collapse of null fluid on the brane

We first obtain the analogue of Vaidya's solution on the brane for studying the collapse of null fluid onto a flat Minkowski cavity on the brane. Since the back-reaction of the bulk onto the brane is supposed to strengthen gravity on the brane, it would favour formation of black hole as against naked singularity. That is the parameter window in the initial data set giving rise to naked singularity in the 4D Vaidya case would now get partially covered.Comment: 12 pages, latex, 3 figures, submitted to Phys.Lett.

On massless 4D Gravitons from 5D Asymptotically AdS Space-times

We investigate the conditions for obtaining four-dimensional massless spin-2 states in the spectrum of fluctuations around an asymptotically $AdS_5$ solution of Einstein-Dilaton gravity. We find it is only possible to have normalizable massless spin-2 modes if the space-time terminates at some IR point in the extra dimension, far from the UV AdS boundary, and if suitable boundary conditions are imposed at the ``end of space.'' In some of these cases the 4D spectrum consists only of a massless spin-2 graviton, with no additional massless or light scalar or vector modes. These spin-2 modes have a profile wave-function peaked in the interior of the 5D bulk space-time. Under the holographic duality, they may be sometimes interpreted as arising purely from the IR dynamics of a strongly coupled QFT living on the AdS boundary.Comment: 40 pages, 1 figure. Revised version, to appear in Nuclear Physics B. Typos corrected, one reference adde

Holographic insights and puzzles

The talk is composed of two parts, both set within the AdS/CFT context. In the first part, I discuss holographic insight into strongly coupled field theory in a black hole background. I conjecture two new gravitational solutions, dubbed black funnels and black droplets, which describe two distinct deconfined phases in the field theory at finite temperature. I also briefly mention puzzles associated with an analogous set-up in a rotating black hole background. In the second part of the talk, I discuss time-dependent states in a CFT on flat spacetime background, exemplified by the conformal soliton flow. Here I focus on puzzles regarding the nature of entropy in time-evolving states and its holographic dual.Comment: 23 pages, 9 figures; prepared for the Proceedings of the XVIth European Workshop on String Theory, Madrid, Spain, June 14-18 201