Dynamic Dilatonic Domain Walls

Motivated by the ``universe as a brane'' idea, we investigate the motion of a $(D-2)$-brane (or domain wall) that couples to bulk matter. Usually one would expect the spacetime outside such a wall to be time dependent however we show that in certain cases it can be static, with consistency of the Israel equations yielding relationships between the bulk metric and matter that can be used as ans\"atze to solve the Einstein equations. As a concrete model we study a domain wall coupled to a bulk dilaton with Liouville potentials for the dilaton both in the bulk and on the wall. The bulk solutions we find are all singular but some have black hole or cosmological horizons, beyond which our solutions describe domain walls moving in time dependent bulks. A significant period of world volume inflation occurs if the potential on the wall is not too steep; in some cases the bulk also inflates (with the wall comoving) while in others the wall moves relative to a non-inflating bulk. We apply our method to obtain cosmological solutions of Ho\v{r}ava-Witten theory compactified on a Calabi-Yau space. tive to a non-inflating bulk. We apply our method to obtain cosmological solutions of Ho\v{r}ava-Witten theory compactified on a Calabi-Yau space.Comment: 32 pages LaTeX, 5 .eps figures, corrected some typo

Supersymmetric AdS5 black holes

The first examples of supersymmetric, asymptotically AdS5, black hole solutions are presented. They form a 1-parameter family of solutions of minimal five-dimensional gauged supergravity. Their angular momentum can never vanish. The solutions are obtained by a systematic analysis of supersymmetric solutions with Killing horizons. Other new examples of such solutions are obtained. These include solutions for which the horizon is a homogeneous Nil or SL(2,R) manifold.Comment: 31 pages. v2: References and calculation of holographic stress tensor added. v3: Solutions preserve 2 supersymmetries. Our original claim that they preserve 4 supersymmetries was based on Ref. [30], which contains a mistake (the general timelike solution preserves 2, not 4, supersymmetries). Nothing else affecte

A Charged Rotating Black Ring

We construct a supergravity solution describing a charged rotating black ring with S^2xS^1 horizon in a five dimensional asymptotically flat spacetime. In the neutral limit the solution is the rotating black ring recently found by Emparan and Reall. We determine the exact value of the lower bound on J^2/M^3, where J is the angular momentum and M the mass; the black ring saturating this bound has maximum entropy for the given mass. The charged black ring is characterized by mass M, angular momentum J, and electric charge Q, and it also carries local fundamental string charge. The electric charge distributed uniformly along the ring helps support the ring against its gravitational self-attraction, so that J^2/M^3 can be made arbitrarily small while Q/M remains finite. The charged black ring has an extremal limit in which the horizon coincides with the singularity.Comment: 25 pages, 1 figur

Quest for Localized 4-D Black Holes in Brane Worlds

We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. It turns out that an exotic, shell-like distribution of matter is required. For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions.Comment: 17 pages, RevTex, 3 figures, version to appear in Physical Review D, comments and references added, typos correcte

Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings

We present new self-gravitating solutions in five dimensions that describe circular strings, i.e., rings, electrically coupled to a two-form potential (as e.g., fundamental strings do), or to a dual magnetic one-form. The rings are prevented from collapsing by rotation, and they create a field analogous to a dipole, with no net charge measured at infinity. They can have a regular horizon, and we show that this implies the existence of an infinite number of black rings, labeled by a continuous parameter, with the same mass and angular momentum as neutral black rings and black holes. We also discuss the solution for a rotating loop of fundamental string. We show how more general rings arise from intersections of branes with a regular horizon (even at extremality), closely related to the configurations that yield the four-dimensional black hole with four charges. We reproduce the Bekenstein-Hawking entropy of a large extremal ring through a microscopic calculation. Finally, we discuss some qualitative ideas for a microscopic understanding of neutral and dipole black rings.Comment: 31 pages, 7 figures. v2: minor changes, added reference. v3: erroneous values of T_{ww} (eq.(3.39)) and n_p (eq.(5.20)) corrected, and accompanying discussion amended. In the journal version these corrections appear as an appended erratum. No major changes involve

Bulk inflaton shadows of vacuum gravity

We introduce a $(5+m)$-dimensional vacuum description of five-dimensional bulk inflaton models with exponential potentials that makes analysis of cosmological perturbations simple and transparent. We show that various solutions, including the power-law inflation model recently discovered by Koyama and Takahashi, are generated from known $(5+m)$-dimensional vacuum solutions of pure gravity. We derive master equations for all types of perturbations, and each of them becomes a second order differential equation for one master variable supplemented by simple boundary conditions on the brane. One exception is the case for massive modes of scalar perturbations. In this case, there are two independent degrees of freedom, and in general it is difficult to disentangle them into two separate sectors.Comment: 22 pages, 4 figures, revtex; v2: references adde

Thermodynamic and gravitational instability on hyperbolic spaces

We study the properties of anti--de Sitter black holes with a Gauss-Bonnet term for various horizon topologies (k=0, \pm 1) and for various dimensions, with emphasis on the less well understood k=-1 solution. We find that the zero temperature (and zero energy density) extremal states are the local minima of the energy for AdS black holes with hyperbolic event horizons. The hyperbolic AdS black hole may be stable thermodynamically if the background is defined by an extremal solution and the extremal entropy is non-negative. We also investigate the gravitational stability of AdS spacetimes of dimensions D>4 against linear perturbations and find that the extremal states are still the local minima of the energy. For a spherically symmetric AdS black hole solution, the gravitational potential is positive and bounded, with or without the Gauss-Bonnet type corrections, while, when k=-1, a small Gauss-Bonnet coupling, namely, \alpha << {l}^2 (where l is the curvature radius of AdS space), is found useful to keep the potential bounded from below, as required for stability of the extremal background.Comment: Shortened to match published (PRD) version, 18 pages, several eps figure

Scaling solution, radion stabilization, and initial condition for brane-world cosmology

We propose a new, self-consistent and dynamical scenario which gives rise to well-defined initial conditions for five-dimensional brane-world cosmologies with radion stabilization. At high energies, the five-dimensional effective theory is assumed to have a scale invariance so that it admits an expanding scaling solution as a future attractor. The system automatically approaches the scaling solution and, hence, the initial condition for the subsequent low-energy brane cosmology is set by the scaling solution. At low energies, the scale invariance is broken and a radion stabilization mechanism drives the dynamics of the brane-world system. We present an exact, analytic scaling solution for a class of scale-invariant effective theories of five-dimensional brane-world models which includes the five-dimensional reduction of the Horava-Witten theory, and provide convincing evidence that the scaling solution is a future attractor.Comment: 17 pages; version accepted for PRD, references adde

Brane World Dynamics and Conformal Bulk Fields

In the Randall-Sundrum scenario we investigate the dynamics of a spherically symmetric 3-brane world when matter fields are present in the bulk. To analyze the 5-dimensional Einstein equations we employ a global conformal transformation whose factor characterizes the $Z_2$ symmetric warp. We find a new set of exact dynamical collapse solutions which localize gravity in the vicinity of the brane for a stress-energy tensor of conformal weight -4 and a warp factor that depends only on the coordinate of the fifth dimension. Geometries which describe the dynamics of inhomogeneous dust and generalized dark radiation on the brane are shown to belong to this set. The conditions for singular or globally regular behavior and the static marginally bound limits are discussed for these examples. Also explicitly demonstrated is complete consistency with the effective point of view of a 4-dimensional observer who is confined to the brane and makes the same assumptions about the bulk degrees of freedom.Comment: 26 pages, latex, no figures. Minor revisions. Some references added. Revised version to appear in Phys. Rev.

Thermodynamics of Gauss-Bonnet black holes revisited

We investigate the Gauss-Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss-Bonnet coupling $c$ and mass $M$, comparing with those of the Born-Infeld-AdS (BIAdS), Reissner-Norstr\"om-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For $c<0$ we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy because the entropy does not satisfy the area-law. On the other hand, for $c>0$, we find the BIAdS-like black hole, showing that the coupling $c$ plays the role of pseudo-charge. Importantly, we could not obtain the SAdS in the limits of $c\to 0$, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasinormal modes may take analytic expressions.Comment: 22 pages, 8 figures, version to appear in EPJ