A topologically flat thick 2-brane on higher dimensional black hole backgrounds

We present a numerical solution for a topologically flat 2-dimensional thick brane on a higher dimensional, spherically symmetric black hole background. Present solution is the last, missing part of the complete set of solutions for the thickness corrected brane-black hole problem in arbitrary number of dimensions. We show that the 2-dimensional case is special compared to all the higher dimensional solutions in the topologically Minkowskian family as being non-analytic at the axis of the system. We provide the numerical solution in the near horizon region and make a comparison with the infinitely thin case.Comment: 9 pages, 4 figures, to appear in Phys. Rev.

Thermodynamics, stability and Hawking-Page transition of Kerr black holes from R\'enyi statistics

Thermodynamics of rotating black holes described by the R\'enyi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the R\'enyi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the R\'enyi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.Comment: 29 pages, 20 figure

Thick brane solutions and topology change transition on black hole backgrounds

We consider static, axisymmetric, thick brane solutions on higher dimensional, spherically symmetric black hole backgrounds. It was found recently [1], that in cases when the thick brane has more than 2 spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a non-perturbative approach. In the present paper we provide an exact, numerical solution of the problem both for black hole- and Minkowski type topologies with arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a 5-dimensional brane embedded in a 6-dimensional bulk.Comment: 11 pages, 10 figures, accepted for publication in Phys. Rev.

Black hole horizons can hide positive heat capacity

Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.Comment: 5 pages, no figures, to be published in Phys. Lett.

Cosmological Perturbations from a Group Theoretical Point of View

We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in terms of irreducible representations of the Lorentz group. The resulting decomposition splits into (scalar, scalar), (scalar, vector) and (vector, vector) terms. These equations directly correspond to the standard Lifshitz classification of cosmological perturbations using scalar, vector and tensor modes which arise from the irreducible SO(3) representation of the spatial part of the metric. While the Lorentz group basis matches the underlying local symmetries of the FLRW spacetime better than the SO(3), the new equations do not provide further simplification compared to the standard cosmological perturbation theory. We conjecture that this is due to the fact that the so(3,1) ~ su(2) x su(2) Lorentz algebra has no pair of commuting generators commuting with any of the translation group generators.Comment: To be published in Classical and Quantum Gravit

Kvázilokális megfigyelhető mennyiségek és az általános relativitáselmálet sugárzási módusinak a vizsgálata = Quasi-local observables and the radiative modes of general relativity

Az Einstein elmélet kvázilokális hamiltoni megfogalmazásában a peremen indukált felületelem rögzitett (`gravitációs szuperszelekciós szektorok') ill. a generátor vektormező divergenciamentes. Minden, a newtoni limeszben is jól viselkedő kvázilokális energiakifejezés a térszerű végtelenben monoton csökkenő kell legyen. Zárt univerzumok teljes tömege pontosan akkor zérus, ha a téridő sik, és e tömeg egybeesik a Sen--Witten operátor négyzetének a legkisebb sajátértékével. Meghatároztuk a Witten féle gauge feltétel kiróhatóságának a feltételeit. Aszimptotikusan sik téridők sugárzási zónájában érvényes globális térbeli impulzusmomentum és a gravitációs sugárzás által szállitott impulzusmomentum-fluxus kifejezést származtattunk. Tetszőleges félegyszerű, nem-abeli mértékcsoportú Yang--Mills mezőkre az elmélet sugárzási zónájában is megmaradó teljes töltés nem létezését bizonyitottuk. Meghatároztuk a kozmikus mikrohullámú háttérsugárzás (CMBR) anizotrópiájának (ill. az indukált hőmérsékletfluktuációknak és ezek időfüggésének) a homogén és izotróp kozmológiai modellek rotációs perturbációitól való függését. Megadtuk a kozmológiai perturbációk egy csoportelméleti tárgyalását. Felső korlátot származtattunk az univerzum rotációs sebességének a mai és a CMBR anyagról történt lecsatolódása idején mérhető értékére. Meghatároztuk tetszőleges dimenziós gömbszimmetrikus brane-fekete lyuk rendszerekben a vastagsági korrekciók általános alakját és a fellépő fázisátalakulás rendjét. | In the quasi-local Hamiltonian formulation of Einstein's theory the area element on the 2-boundary is shown to be fixed (`gravitational superselection sectors') and the generator vector field is divergence free. Any quasi-local energy expression that behaves in the correct way in the Newtonian limit must be decreasing at spatial infinity. The total mass of closed universes is shown to be zero precisely when the spacetime is flat, and it coincides with the smallest eigenvalue of the square of the Sen--Witten operator. We determined the conditions under which Witten's gauge condition can be imposed. An expression for the total spatial angular momentum and the corresponding flux in the radiative zone of asymptotically flat spacetimes. are given. In any Yang--Mills theory with non-Abelian semi-simple gauge group there exists no total charge that would be conserved in the radiative zone. We determined the dependence of the anisotropy of the cosmic microwave background radiation (CMBR) (and the induced temperature fluctuations and their time dependence) on the rotational perturbations of homogeneous and isotropic cosmological models. We developed a group theoretical treatment of cosmological perturbations. We derived an upper bound on the rotational velocity of the universe at the time of decoupling of CMBR from the matter. In spherically symmetric brane black hole systems we determined the general form of the thickness corrections and the order of the phase transition

Covariant Linear Perturbations in a Concordance Model

We present the complete solution of the first order metric and density perturbation equations in a spatially flat (K=0), Friedmann-Robertson-Walker (FRW) universe filled with pressureless ideal fluid, in the presence of cosmological constant. We use covariant linear perturbation formalism and the comoving gauge condition to obtain the field and conservation equations. The solution contains all modes of the perturbations, i.e. scalar, vector and tensor modes, and we show that our results are in agreement with the Sachs & Wolfe metric perturbation formalism.Comment: 8 page

Revisiting Rotational Perturbations and the Microwave Background

We consider general-relativistic rotational perturbations in homogeneous and isotropic Friedman - Robertson - Walker (FRW) cosmologies. Taking linear perturbations of FRW models, the general solution of the field equations contains tensorial, vectorial and scalar functions. The vectorial terms are in connection with rotations in the given model and due to the Sachs - Wolfe effect they produce contributions to the temperature fluctuations of the cosmic microwave background radiation (CMBR). In present paper we obtain the analytic time dependence of these contributions in a spatially flat, FRW model with pressureless ideal fluid, in the presence and the absence of a cosmological constant. We find that the solution can be separated into an integrable and a non-integrable part as is the situation in the case of scalar perturbations. Analyzing the solutions and using the results of present observations we estimate the order of magnitude of the angular velocity corresponding to the rotation tensor at the time of decoupling and today.Comment: accepted for publication in Int. J. Mod. Phys.