Relativistic non-equilibrium thermodynamics revisited

Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.Comment: 11 pages, no figure

Low energy effective gravitational equations on a Gauss-Bonnet brane

We present effective gravitational equations at low energies in a $Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.Comment: 10 pages, v2: minor clarification

Interior of Distorted Black Holes

We study the interior of distorted static axisymmetric black holes. We obtain a general interior solution and study its asymptotics both near the horizon and singularity. As a special example, we apply the obtained results to the case of the so-called `caged' black holes.Comment: 12 pages, 16 figure

Inverse Square Law of Gravitation in (2+1)-Dimensional Space-Time as a Consequence of Casimir Energy

The gravitational effect of vacuum polarization in space exterior to a particle in (2+1)-dimensional Einstein theory is investigated. In the weak field limit this gravitational field corresponds to an inverse square law of gravitational attraction, even though the gravitational mass of the quantum vacuum is negative. The paradox is resolved by considering a particle of finite extension and taking into account the vacuum polarization in its interior.Comment: 10 pages, LaTeX, Report: UPR-0540-T, To appear in Physica Script

Two-dimensional Quantum Black Holes, Branes in BTZ and Holography

We solve semiclassical Einstein equations in two dimensions with a massive source and we find a static, thermodynamically stable, quantum black hole solution in the Hartle-Hawking vacuum state. We then study the black hole geometry generated by a boundary mass sitting on a non-zero tension 1-brane embedded in a three-dimensional BTZ black hole. We show that the two geometries coincide and we extract, using holographic relations, information about the CFT living on the 1-brane. Finally, we show that the quantum black hole has the same temperature of the bulk BTZ, as expected from the holographic principle.Comment: 10 pages, 2 figures, RevTex, ``point particle of mass \mu '' changed with ``massive boundary source'' for better clarity. Action in (50) written in Z_2 symmetric form. Appendix clarified. Minor corrections and references added. Version accepted for pubblication in PRD15 (2006

A Comment on Junction and Energy Conditions in Thin Shells

This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte

High-energy effective theory for matter on close Randall Sundrum branes

Extending the analysis of hep-th/0504128, we obtain a formal expression for the coupling between brane matter and the radion in a Randall-Sundrum braneworld. This effective theory is correct to all orders in derivatives of the radion in the limit of small brane separation, and, in particular, contains no higher than second derivatives. In the case of cosmological symmetry the theory can be obtained in closed form and reproduces the five-dimensional behaviour. Perturbations in the tensor and scalar sectors are then studied. When the branes are moving, the effective Newtonian constant on the brane is shown to depend both on the distance between the branes and on their velocity. In the small distance limit, we compute the exact dependence between the four-dimensional and the five-dimensional Newtonian constants.Comment: Updated version as published in PR

Massless and massive graviton spectra in anisotropic dilatonic braneworld cosmologies

We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spectral amplitude, which can become dominant in the total spectrum. The presence of the dilaton, on the contrary, decrease the relative importance of the massive modes.Comment: 18 pages, 4 figures, Typos correction

Lorentzian and signature changing branes

General hypersurface layers are considered in order to describe brane-worlds and shell cosmologies. No restriction is placed on the causal character of the hypersurface which may thus have internal changes of signature. Strengthening the results in our previous letter [1], we confirm that a good, regular and consistent description of signature change is achieved in these brane/shells scenarios, while keeping the hypersurface and the bulk completely regular. Our formalism allows for a unified description of the traditional timelike branes/shells together with the signature-changing, or pure null, ones. This allows for a detailed comparison of the results in both situations. An application to the case of hypersurface layers in static bulks is presented, leading to the general Robertson-Walker geometry on the layer --with a possible signature change. Explicit examples on anti de Sitter bulks are then studied. The permitted behaviours in different settings ($Z_{2}$-mirror branes, asymmetric shells, signature-changing branes) are analysed in detail. We show in particular that (i) in asymmetric shells there is an upper bound for the energy density, and (ii) that the energy density within the brane vanishes when approaching a change of signature. The description of a signature change as a `singularity' seen from within the brane is considered. We also find new relations between the fundamental constants in the brane/shell, its tension, and the cosmological and gravitational constants of the bulk, independently of the existence or not of a change of signature.Comment: 23 pages, 2 figure