Exact solutions of Dirac equation on (1+1)-dimensional spacetime coupled to a static scalar field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.Comment: 7 pages, Late

The black hole final state

We propose that in quantum gravity one needs to impose a final state boundary condition at black hole singularities. This resolves the apparent contradiction between string theory and semiclassical arguments over whether black hole evaporation is unitary.Comment: 17 pages, harvmac, 1 figure, v2: comment about interactions and references adde

Phase Transition of Electrically Charged Ricci-flat Black Holes

We study phase transition between electrically charged Ricci-flat black holes and AdS soliton spacetime of Horowitz and Myers in five dimensions. Boundary topology for both of them is $S^1 \times S^1 \times R^2$. We consider Reissner-Nordstrom black hole and R-charged black holes and find that phase transition of these black holes to AdS soliton spacetime depends on the relative size of two boundary circles. We also perform the stability analysis for these black holes. In order to use the AdS/CFT correspondence, we work in the grand canonical ensemble.Comment: 33 pages, 9 figures, Version 2, References adde

Nuttier Bubbles

We construct new explicit solutions of general relativity from double analytic continuations of Taub-NUT spacetimes. This generalizes previous studies of 4-dimensional nutty bubbles. One 5-dimensional locally asymptotically AdS solution in particular has a special conformal boundary structure of $AdS_3\times S^1$. We compute its boundary stress tensor and relate it to the properties of the dual field theory. Interestingly enough, we also find consistent 6-dimensional bubble solutions that have only one timelike direction. The existence of such spacetimes with non-trivial topology is closely related to the existence of the Taub-NUT(-AdS) solutions with more than one NUT charge. Finally, we begin an investigation of generating new solutions from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality, we provide new explicit time-dependent backgrounds in six dimensions.Comment: 32 pages, 1 figure; v.3. typos corrected. Matches the published versio

Instability of generalised AdS black holes and thermal field theory

We study black holes in AdS-like spacetimes, with the horizon given by an arbitrary positive curvature Einstein metric. A criterion for classical instability of such black holes is found in the large and small black hole limits. Examples of large unstable black holes have a B\"ohm metric as the horizon. These, classically unstable, large black holes are locally thermodynamically stable. The gravitational instability has a dual description, for example by using the $AdS_7 \times S^4$ version of the AdS/CFT correspondence. The instability corresponds to a critical temperature of the dual thermal field theory defined on a curved background.Comment: 1+16 pages. 1 figure. LaTeX. Minor clarification

Arrow of time in a recollapsing quantum universe

We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects in the region of the classical turning point. Since gravitational time dilation diverges at horizons, collapsing matter must then start re-expanding ``anticausally" (controlled by the reversed arrow) before horizons or singularities can form. We also discuss the meaning of the time-asymmetric expression used in the definition of ``consistent histories". We finally emphasize that there is no mass inflation nor any information loss paradox in this scenario.Comment: Many conceptual clarifications include

Classical and Thermodynamic Stability of Black Branes

It is argued that many non-extremal black branes exhibit a classical Gregory-Laflamme instability if, and only if, they are locally thermodynamically unstable. For some black branes, the Gregory-Laflamme instability must therefore disappear near extremality. For the black $p$-branes of the type II supergravity theories, the Gregory-Laflamme instability disappears near extremality for $p=1,2,4$ but persists all the way down to extremality for $p=5,6$ (the black D3-brane is not covered by the analysis of this paper). This implies that the instability also vanishes for the near-extremal black M2 and M5-brane solutions.Comment: 21 pages, LaTeX. v2: Various points clarified, typos corrected and reference adde

Glassy Phase Transition and Stability in Black Holes

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest's scheme we further prove that this is a glassy phase transition with a Prigogine-Defay ratio close to 3. This value is well placed within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.Comment: v3, minor changes over v2, references added, LaTeX-2e, 18 pages, 3 ps figures, to appear in Eour. Phys. Jour.

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Two-dimensional Quantum-Corrected Eternal Black Hole

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.Comment: Latex, 28 pges; minor corrections in text and abstract made and new references adde