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Item Nonlinearly charged Lifshitz black holes for any exponent z > 1Autores: Alvarez, A.; Ayon-Beato, E.; Gonzalez, HA.; Hassaine, M.Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension D are known only if the dynamical critical exponent is fixed as z = 2(D - 2). In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent z > 1 by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called ( , P )-formalism and obtain a family of charged black hole solutions depending on two parameters. We also remark that the value of the dynamical exponent z = D - 2 turns out to be critical in the sense that it yields asymptotically Lifshitz black holes with logarithmic decay supported by a particular logarithmic electrodynamics. All these configurations include extremal Lifshitz black holes. Charged topological Lifshitz black holes are also shown to emerge by slightly generalizing the proposed electrodynamics.Item Supersymmetry of a different kindAutores: Alvarez, P.D.; Valenzuela, M.; Zanelli, J.A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersymmetry. Although the supersymmetry is locally realized, there is no spin-3/2 gravitino, and is therefore not supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, the fermion may acquire mass through the coupling with geometry, while the bosons - the U(1) field and the spin connection - remain massless.
