Gravitational Properties of Monopole Spacetimes Near the Black Hole Threshold

Although nonsingular spacetimes and those containing black holes are qualitatively quite different, there are continuous families of configurations that connect the two. In this paper we use self-gravitating monopole solutions as tools for investigating the transition between these two types of spacetimes. We show how causally distinct regions emerge as the black hole limit is achieved, even though the measurements made by an external observer vary continuously. We find that near-critical solutions have a naturally defined entropy, despite the absence of a true horizon, and that this has a clear connection with the Hawking-Bekenstein entropy. We find that certain classes of near-critical solutions display naked black hole behavior, although they are not truly black holes at all. Finally, we present a numerical simulation illustrating how an incident pulse of matter can induce the dynamical collapse of a monopole into an extremal black hole. We discuss the implications of this process for the third law of black hole thermodynamics.Comment: 23 pages, 4 figures RevTe

Do stringy corrections stabilize coloured black holes?

We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically charged black holes while the bulk of the neutral black holes are proven to be stable under small, gauge-dependent perturbations. Finally, the electrically charged black holes are found to be characterized only by the existence of a gravitational sector of perturbations. As in the case of neutral black holes, we demonstrate that for the bulk of electrically charged black holes no unstable modes arise in this sector.Comment: 17 pages, Revtex, comments and a reference added, version to appear in Physical Review

Stability of self-gravitating magnetic monopoles

The stability of a spherically symmetric self-gravitating magnetic monopole is examined in the thin wall approximation: modeling the interior false vacuum as a region of de Sitter space; the exterior as an asymptotically flat region of the Reissner-Nordstr\"om geometry; and the boundary separating the two as a charged domain wall. There remains only to determine how the wall gets embedded in these two geometries. In this approximation, the ratio $k$ of the false vacuum to surface energy densities is a measure of the symmetry breaking scale $\eta$. Solutions are characterized by this ratio, the charge on the wall $Q$, and the value of the conserved total energy $M$. We find that for each fixed $k$ and $Q$ up to some critical value, there exists a unique globally static solution, with $M\simeq Q^{3/2}$; any stable radial excitation has $M$ bounded above by $Q$, the value assumed in an extremal Reissner-Nordstr\"om geometry and these are the only solutions with $M<Q$. As $M$ is raised above $Q$ a black hole forms in the exterior: (i) for low $Q$ or $k$, the wall is crushed; (ii) for higher values, it oscillates inside the black hole. If the mass is not too high these `collapsing' solutions co-exist with an inflating bounce; (iii) for $k$, $Q$ or $M$ outside the above regimes, there is a unique inflating solution. In case (i) the course of the bounce lies within a single asymptotically flat region (AFR) and it resembles closely the bounce exhibited by a false vacuum bubble (with Q=0). In cases (ii) and (iii) the course of the bounce spans two consecutive AFRs.Comment: 19 pages, RevTex two cols., 11 eps figs. Submitted to Phys. Rev.

Black hole solutions in Euler-Heisenberg theory

We construct static and spherically symmetric black hole solutions in the Einstein-Euler-Heisenberg (EEH) system which is considered as an effective action of a superstring theory. We considered electrically charged, magnetically charged and dyon solutions. We can solve analytically for the magnetically charged case. We find that they have some remarkable properties about causality and black hole thermodynamics depending on the coupling constant of the EH theory $a$ and $b$, though they have central singularity as in the Schwarzschild black hole.Comment: 8 pages, 13 figures, figures corrected and some comments adde

Perturbations of global monopoles as a black hole's hair

We study the stability of a spherically symmetric black hole with a global monopole hair. Asymptotically the spacetime is flat but has a deficit solid angle which depends on the vacuum expectation value of the scalar field. When the vacuum expectation value is larger than a certain critical value, this spacetime has a cosmological event horizon. We investigate the stability of these solutions against the spherical and polar perturbations and confirm that the global monopole hair is stable in both cases. Although we consider some particular modes in the polar case, our analysis suggests the conservation of the "topological charge" in the presence of the event horizons and violation of black hole no-hair conjecture in asymptotically non-flat spacetime.Comment: 11 pages, 2 figures, some descriptions were improve

Dyonic BIon black hole in string inspired model

We construct static and spherically symmetric particle-like and black hole solutions with magnetic and/or electric charge in the Einstein-Born-Infeld-dilaton-axion system, which is a generalization of the Einstein-Maxwell-dilaton-axion (EMDA) system and of the Einstein-Born-Infeld (EBI) system. They have remarkable properties which are not seen for the corresponding solutions in the EMDA and the EBI system.Comment: 13 pages, 15 figures, Final version in PR

Composition of Haar Paraproducts: The Random Case

When is the composition of paraproducts bounded? This is an important, and difficult question, related to to a question of Sarason on composition of Hankel matrices, and the two-weight problem for the Hilbert transform. We consider randomized variants of this question, finding non-classical characterizations, for dyadic paraproducts.Comment: 13 pages. Submitted. v2: \showkeys commented out, with other minor change

Dilatonic Black Holes with Gauss-Bonnet Term

We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged and a ``colored'' black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find critical point and a singular end point. Below the mass corresponding to the critical point, nosolution exists, while the curvature on the horizon diverges and anaked singularity appears at the singular point. A cusp structure in the mass-entropy diagram is found at the critical point and black holes on the branch between the critical and singular points become unstable. For magnetically charged and ``colored" black holes, the solution becomes singular just at the end point with a finite mass. Because the black hole temperature is always finite even at the critical point or the singular point, we may conclude that the evaporation process will not be stopped even at the critical point or the singular point, and the black hole will move to a dynamical evaporation phase or a naked singularity will appear.Comment: 31pages, 11figures, LaTex styl

Non-Abelian Black Holes and Catastrophe Theory I : Neutral Type

We re-analyze the globally neutral non-Abelian black holes and present a unified picture, classifying them into two types; Type I (black holes with massless non-Abelian field) and Type II (black holes with ``massive" non-Abelian field). For the Type II, there are two branches: The black hole in the high-entropy branch is ``stable" and almost neutral, while that in the low entropy branch, which is similar to the Type I, is unstable and locally charged. To analyze their stabilities, we adopt the catastrophe theoretic method, which reveals us a universal picture of stability of the black holes. It is shown that the isolated Type II black hole has a fold catastrophe structure. In a heat bath system, the Type I black hole shows a cusp catastrophe, while the Type II has both fold and cusp catastrophe.Comment: 27pages, LaTex style, WU-AP/39/94. Figures are available (hard copies) upon requests [[email protected] (T.Torii)

Non-Abelian Black Holes in Brans-Dicke Theory

We find a black hole solution with non-Abelian field in Brans-Dicke theory. It is an extension of non-Abelian black hole in general relativity. We discuss two non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and the SU(2)$\times$SU(2) Skyrme field. In both cases, as in general relativity, there are two branches of solutions, i.e., two black hole solutions with the same horizon radius. Masses of both black holes are always smaller than those in general relativity. A cusp structure in the mass-horizon radius ($M_{g}$-$r_{h}$) diagram, which is a typical symptom of stability change in catastrophe theory, does not appear in the Brans-Dicke frame but is found in the Einstein conformal frame. This suggests that catastrophe theory may be simply applied for a stability analysis as it is if we use the variables in the Einstein frame. We also discuss the effects of the Brans-Dicke scalar field on black hole structure.Comment: 31 pages, revtex, 21 figure