Cosmological Black Holes on Branes

We examined analytically a cosmological black hole domain wall system. Using the C-metric construction we derived the metric for the spacetime describing an infinitely thin domain wall intersecting a cosmological black hole. We studied the behaviour of the scalar field describing a self-interacting cosmological domain wall and find the approximated solution valid for large distances. The thin wall approximation and the back raection problem were elaborated finding that the topological kink solution smoothed out singular behaviour of the zero thickness wall using a core topological and hence thick domain wall. We also analyze the nucleation of cosmological black holes on and in the presence of a domain walls and conclude that the domain wall will nucleate small black holes on it rather than large ones inside.Comment: 13 pages, Revtex, to be published in Phys.Rev. D1

Gauge-invariant fluctuations of scalar branes

A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schr\"odinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and and vector fluctuations exhibit non normalizable zero modes and are, consequently, not localized on the brane. The spectrum of the massive modes of the fluctuations is analyzed using supersymmetric quantum mechanics.Comment: 29 pages in Latex styl

Brane-world creation and black holes

An inflating brane-world can be created from ``nothing'' together with its Anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap $m=(3/2) H$, where $H$ is the Hubble rate. We consider the analog of the Nariai solution and argue that it describes pair production of ``Black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing, or the production of AdS black holes in the vicinity of a pre-existing inflating brane-world. The Lorentzian evolution of the brane-world after creation is briefly discussed. An additional "integration constant" in the Friedmann equation -accompanying a term which dilutes like radiation- describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. This could be a 5-dimensional black hole or a "parallel" brane-world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the $AdS/CFT$ correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.Comment: 15 pages, 2 figures, LaTeX. References added, typos corrected, added Comment on AdS/CFT correspondenc

Static black holes with a negative cosmological constant: Deformed horizon and anti-de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild-anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild-anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).Comment: 31 pages, 5 figures, one reference added, to be published in PR

Black Holes and Instabilities of Negative Tension Branes

We consider the collision in 2+1 dimensions of a black hole and a negative tension brane on an orbifold. Because there is no gravitational radiation in 2+1 dimensions, the horizon area shrinks when part of the brane falls through. This provides a potential violation of the generalized second law of thermodynamics. However, tracing the details of the dynamical evolution one finds that it does not proceed from equilibrium configuration to equilibrium configuration. Instead, a catastrophic space-time singularity develops similar to the `big crunch' of $\Omega >1$ FRW space-times. In the context of classical general relativity, our result demonstrates a new instability of constructions with negative tension branes.Comment: 18 pages, 3 figures, uses RevTeX. Minor typos fixed. References and one footnote adde

Large Extra Dimensions and Cosmological Problems

We consider a variant of the brane-world model in which the universe is the direct product of a Friedmann, Robertson-Walker (FRW) space and a compact hyperbolic manifold of dimension $d\geq2$. Cosmology in this space is particularly interesting. The dynamical evolution of the space-time leads to the injection of a large entropy into the observable (FRW) universe. The exponential dependence of surface area on distance in hyperbolic geometry makes this initial entropy very large, even if the CHM has relatively small diameter (in fundamental units). This provides an attractive reformulation of the cosmological entropy problem, in which the large entropy is a consequence of the topology, though we would argue that a final solution of the entropy problem requires a dynamical explanation of the topology of spacetime. Nevertheless, it is reassuring that this entropy can be achieved within the holographic limit if the ordinary FRW space is also a compact hyperbolic manifold. In addition, the very large statistical averaging inherent in the collapse of the initial entropy onto the brane acts to smooth out initial inhomogeneities. This smoothing is then sufficient to account for the current homogeneity of the universe. With only mild fine-tuning, the current flatness of the universe can also then be understood. Finally, recent brane-world approaches to the hierarchy problem can be readily realized within this framework.Comment: 15 pages, 1 figure. Revised and corrected discussions of the entropy problem. New references adde

Challenges and Obstacles for a Bouncing Universe in Brane Models

A Brane evolving in the background of a charged AdS black-hole displays in general a bouncing behaviour with a smooth transition from a contracting to an expanding phase. We examine in detail the conditions and consequences of this behaviour in various cases. For a cosmological-constant-dominated Brane, we obtain a singularity-free, inflationary era which is shown to be compatible only with an intermediate-scale fundamental Planck mass. For a radiation-dominated Brane, the bouncing behaviour can occur only for background-charge values exceeding those allowed for non-extremal black holes. For a matter-dominated Brane, the black-hole mass affects the proper volume or the expansion rate of the Brane. We also consider the Brane evolving in an asymmetric background of two distinct charged AdS black hole spacetimes being bounded by the Brane and find that, in the case of an empty critical Brane, bouncing behaviour occurs only if the black-hole mass difference is smaller than a certain value. The effects of a Brane curvature term on the bounce at early and late times are also investigated.Comment: 23 pages, Latex file, comments and references added, version to appear in Phys. Rev.

Black Holes in Higher-Dimensional Gravity

These lectures review some of the recent progress in uncovering the phase structure of black hole solutions in higher-dimensional vacuum Einstein gravity. The two classes on which we focus are Kaluza-Klein black holes, i.e. static solutions with an event horizon in asymptotically flat spaces with compact directions, and stationary solutions with an event horizon in asymptotically flat space. Highlights include the recently constructed multi-black hole configurations on the cylinder and thin rotating black rings in dimensions higher than five. The phase diagram that is emerging for each of the two classes will be discussed, including an intriguing connection that relates the phase structure of Kaluza-Klein black holes with that of asymptotically flat rotating black holes.Comment: latex, 49 pages, 5 figures. Lectures to appear in the proceedings of the Fourth Aegean Summer School, Mytiline, Lesvos, Greece, September 17-22, 200

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc