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In this work we study the thermodynamics of a ($2+1$)-dimensional static black hole under a nonlinear electric field. In addition to standard approaches, we investigate black hole thermodynamic geometry. We compute Weinhold and Ruppeiner metrics and compare the thermodynamic geometries with the standard description for black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. For thermodynamic equilibrium in three-dimensional space, we compute heat engine efficiency and show that it may be constructed with this black hole.

We reconsider the cosmological model discussed by Sung-Won Kim [Phys. Rev D 53, 6889 (1996)] in the context of Friedmann-Robertson-Walker cosmologies with a traversable wormhole, where it is assumed that the matter content is divided into two parts: the cosmic part that depends on time only and the wormhole part that depends on space only. The cosmic part obeys the barotropic equation of state $p_c=\gamma \rho_c$. The complete analysis requires further care and reveals more interesting results than what was previously shown by the author. They can be readily applied to the evolution of a large class of cosmological models which are more general than FRW models., Comment: 4 pages, To be published in Physical Review D

We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state \omega=p/\rho < -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense than in cosmology, where the phantom energy is considered a homogeneously distributed fluid. Specifically, for some static wormhole geometries the phantom matter was considered as an inhomogeneous and anisotropic fluid, with radial and lateral pressures satisfying the relations $p_{r}/\rho, Comment: 9 pages, 9 figures, accepted for publication in Phys. Rev. D

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with the help of the procedure used in Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnetic field are separately studied and their corresponding solutions found., Comment: 8 pages, LaTeX, no figures, to appear in Physical Review D

In this work we establish the correspondence between solutions to the Friedmann-Robertson-Walker cosmologies for perfect fluid and scalar field sources, where both satisfy state equations of the form $p+\ensuremath{\rho}=\ensuremath{\gamma}f(\ensuremath{\rho}),$ not necessarily linear ones. Such state equations are of common use in the case of matter fluids; nevertheless, for a scalar field, they introduce relationships on the potential and kinetic scalar field energies which restrict the set of solutions. A theorem in this respect is demonstrated: From any given $3+1$ cosmological solution, obeying the quoted state equations, one can derive its $2+1$ cosmological counterpart or vice versa. Some applications are given.

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincar\`{e} translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451., Comment: 7 pages, Latex, accepted in Phys. Rev. D