Mauricio Cataldo

Viscous dark energy and phantom evolution

Abstract In order to study if the bulk viscosity may induce a big rip singularity on the flat FRW cosmologies, we investigate dissipative processes in the universe within the framework of the standard Eckart theory of relativistic irreversible thermodynamics, and in the full causal Israel–Stewart–Hiscock theory. We have found cosmological solutions which exhibit, under certain constraints, a big rip singularity. We show that the negative pressure generated by the bulk viscosity cannot avoid that the dark energy of the universe to be phantom energy.

Three dimensional black hole coupled to the Born-Infeld electrodynamics

Abstract A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained Einstein-Born-Infeld solution for certain range of the parameters (mass, charge, cosmological and the Born-Infeld constants) represent a static circularly symmetric black hole. Although the covariant metric components and the electric field do not exhibit a singular behavior at r =0 the curvature invariants are singular at that point.

Holographic principle and the dominant energy condition for Kasner type metrics

Abstract In this Letter we study adiabatic anisotropic matter filled Bianchi type I models of the Kasner form together with the cosmological holographic bound. We find that the dominant energy condition and the holographic bound give precisely the same constraint on the scale factor parameters that appear in the metric.

Regular (2+1)-dimensional black holes within nonlinear electrodynamics

(2+1)-regular static black hole solutions with a nonlinear electric field are derived. The source to the Einstein equations is an energy momentum tensor of nonlinear electrodynamics, which satisfies the weak energy conditions and in the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class of solutions is regular; the metric, curvature invariants and electric field are regular everywhere. The metric becomes, for a vanishing parameter, the (2+1)-static charged BTZ solution. A general procedure to derive solutions for the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the electric field is formulated; for relevant electric fields one requires the fulfillment of the weak energy conditions.

Interacting cosmic fluids in power-law Friedmann-Robertson-Walker cosmological models

Abstract We provide a detailed description for power-law scaling Friedmann–Robertson–Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the two fluids, neither component is conserved separately and the energy densities are proportional to 1 / t 2 . It is shown that in flat FRW cosmological models there can exist interacting superpositions of two perfect fluids (each of them having a positive energy density) which accelerate the expansion of the universe. In this family there also exist flat power-law cosmological scenarios where one of the fluids may have a “cosmological constant” or “vacuum energy” equation of state ( p = − ρ ) interacting with the other component; this scenario exactly mimics the behavior of the standard flat Friedmann solution for a single fluid with a barotropic equation of state. These possibilities of combining interacting perfect fluids do not exist for the non-interacting mixtures of two perfect cosmic fluids, where the general solution for the scale factor is not described by power-law expressions and has a more complicated behavior. In this study is considered also the associated single fluid model interpretation for the interaction between two fluids.

Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime

Abstract The fundamental metrics, which describe any static three-dimensional Einstein–Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic field: two for the vector electric field and one for the scalar magnetic field. It is shown that we cannot have any superposition of these components of the electric and magnetic fields in this kind of static gravitational field. One of the electrostatic Einstein–Maxwell solutions is related to the magnetostatic solution by a duality mapping, while the second electrostatic gravitational field must be solved separately. Solutions induced by the more general (2+1)-Maxwell tensor on the static cylindrically symmetric spacetimes are studied and it is shown that all of them are also connected by duality mappings.

Self-dual Lorentzian wormholes in n-dimensional Einstein gravity

A family of spherically symmetric, static and self-dual Lorentzian wormholes is ob- tained in n-dimensional Einstein gravity. This class of solutions includes the n-dimensional versions of the Schwarzschild black hole and the spatial-Schwarzschild traversable wormhole. Using isotropic coordinates we study the geometrical structure of the solution, and delineate the domains of the free parameters for which wormhole, naked singular geometries and the Schwarzschild black hole are obtained. It is shown that, in the lower dimensional Einstein gravity without cosmological constant, we can not have self-dual Lorentzian wormholes.

(2+1)-dimensional black hole with Coulomb-like field

Abstract A (2+1)-static black hole solution with a nonlinear electric field is derived. The source to the Einstein equations is a nonlinear electrodynamics, satisfying the weak energy conditions, and it is such that the energy momentum tensor is traceless. The obtained solution is singular at the origin of coordinates. The derived electric field E ( r ) is given by E ( r )= q / r 2 , thus it has the Coulomb form of a point charge in the Minkowski spacetime. This solution describes charged (anti)-de Sitter spaces. An interesting asymptotically flat solution arises for Λ =0.

THREE DIMENSIONAL EXTREME BLACK HOLE WITH SELF (ANTI-SELF) DUAL MAXWELL FIELD

Abstract The most general charged version of the spinning BTZ black hole solution assuming an (anti-) self dual condition imposed on the orthonormal basis components of the electric and magnetic fields is obtained. It is found that the one-parameter Kamata-Koikawa field is a particular solution of our general solution. A spinning magnetic solution is also found. It is shown that a duality mapping exists among spinning solutions obtained from electrostatic and magnetostatic fields with the help of the local transformation t→t−ωθ, θ→θ−ωt .

Evolving Lorentzian wormholes supported by phantom matter and cosmological constant

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constant we have wormholes which expand forever and, for negative cosmological constant we have wormholes which expand to a maximum value and then recollapse. At spatial infinity the energy density and the pressures of the anisotropic phantom matter threading the wormholes vanish; thus these evolving wormholes are asymptotically vacuum {lambda}-Friedmann models with either open or closed or flat topologies.