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
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.
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. Keywords: 2+1 dimensions, Non-Linear black hole PACS numbers: 04.20.JbMost of the papers on 2+1-solutions coupled to electromagnetic fields are done for Maxwell electrodynamics [1,4], i.e. the electromagnetic tensor is derived, in 2+1 theory, from a Lagrangian which is proportional to the single invariant, namely L ∝ F , with F = 1 4 F µν F µν . On the other hand, the introduction of electrodynamics of nonlinear type [5][6][7] , where the dependence on the invariant is enlarged, has proved to be fruitful [8].In 3+1 electromagnetism, the Maxwell energy momentum tensor is given byand consequently is trace free. If one constructs a nonlinear electrodynamics based on the invariant F , i.e. L = L(F ), the resulting energy momentum tensor is given asThus, if one demands that the trace to be vanished, i.e. T = 0, we find that L F −F L = 0, whose solution is L ∝ F . In Minkowski spacetime the Maxwell theory is singled out among all nonlinear theories by the vanishing of the trace. Recall that in 3+1 there is a second invariant -a pseudoscalarG = 1 4 * F µν F µν , where ⋆ stands for the duality operation. We may include into the Lagrangian for building up a wider nonlinear theories in which the Born-Infeld electrodynamics [9]is an example.In 2+1 spacetime, the Maxwell energy momentum tensor is of the same form as in 3+1 dimensions, but the * E-mail address: mcataldo@alihuen.ciencias.ubiobio.cl † E-mail address: ncruz@lauca.usach.cl ‡ E-mail address: sdelcamp@ucv.cl § E-mail address: alberto.garcia@fis.cinvestav.mx trace contrary of the 3+1 case occurs to be non-vanishing, i.e. T = F/4π = 0. Hence, this 2+1 Maxwell theory has always trace. The electric field for a static circularly symmetric metric coupled to a Maxwell field occurs to be proportional to the inverse of r, i.e. E(r) ∝ 1/r, hence the potential A 0 is logarithmic, i.e. A 0 ∝ ln r, and consequently blows up at r = 0 and r going to infinity. In this paper we are interested in electromagnetic theories in which the energy momentum tensor is traceless. This condition restricts the class of nonlinear electrodynamics to be studied. Incidentally the traceless nonlinear electrodynamics, in 2+1 dimensions, occurs to be unique with Lagrangian proportional to F 3/4 . Restricting our study to a static circularly symmetric metric, the resulting electromagnetic field for this theory surprisingly is proportional to the inverse of r 2 , i.e. a Coulomb law for a point charge in 3+1 Minkowski space. Moreover, the e...
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.
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