Surveying the Three-Dimensional Fixed Points of T-Duality

We explore the family of fixed points of T-Duality transformations in three dimensions. For the simplest nontrivial self-duality conditions it is possible to show that, additionally to the spacelike isometry in which the T-Duality transformation is performed, these backgrounds must be necessarily stationary. This allows to prove that for nontrivial string coupling, the low energy bosonic string backgrounds which are additionally self-T-dual along an isometry direction generated by a constant norm Killing vector are uniquely described by a two-parametric class, including only three nonsingular cases: the charged black string, the exact gravitational wave propagating along the extremal black string, and the flat space with a linear dilaton. Besides, for constant string coupling, the only self-T-dual lower energy string background under the same assumptions corresponds to the Coussaert-Henneaux spacetime. Thus, we identify minimum criteria that yield a classification of these quoted examples and only these. All these T-dual fixed points describe exact backgrounds of string theory.Comment: 11 Page

Scalar Fields Nonminimally Coupled to pp Waves

Here, we report pp waves configurations of three-dimensional gravity for which a scalar field nonminimally coupled to them acts as a source. In absence of self-interaction the solutions are gravitational plane waves with a profile fixed in terms of the scalar wave. In the self-interacting case, only power-law potentials parameterized by the nonminimal coupling constant are allowed by the field equations. In contrast with the free case the self-interacting scalar field does not behave like a wave since it depends only on the wave-front coordinate. We address the same problem when gravitation is governed by topologically massive gravity and the source is a free scalar field. From the pp waves derived in this case, we obtain at the zero topological mass limit, new pp wave solutions of conformal gravity for any arbitrary value of the nonminimal coupling parameter. Finally, we extend these solutions to the self-interacting case of conformal gravity.Comment: 14 pages, RevTeX. Minor changes. To appear in Phys. Rev.

pp Waves of Conformal Gravity with Self-Interacting Source

Recently, Deser, Jackiw and Pi have shown that three-dimensional conformal gravity with a source given by a conformally coupled scalar field admits pp wave solutions. In this letter, we consider this model with a self-interacting potential preserving the conformal structure. A pp wave geometry is also supported by this system and, we show that this model is equivalent to topologically massive gravity with a cosmological constant whose value is given in terms of the potential strength.Comment: 6 pages, minor changes, accepted in Ann. Phy

Smarr's formula for black holes with non-linear electrodynamics

It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.Comment: 10 pages, 3 figures.Contribution to the Festscrift of Prof. A. Garci

Higher-dimensional AdS waves and pp-waves with conformally related sources

AdS waves and pp-waves can only be supported by pure radiation fields, for which the only nonvanishing component of the energy-momentum tensor is the energy density along the retarded time. We show that the nonminimal coupling of self-gravitating scalar fields to the higher-dimensional versions of these exact gravitational waves can be done consistently. In both cases, the resulting pure radiation constraints completely fix the scalar field dependence and the form of the allowed self-interactions. More significantly, we establish that the two sets of pure radiation constraints are conformally related for any nonminimal coupling, in spite of the fact that the involved gravitational fields are not necessarily related. In this correspondence, the potential supporting the AdS waves emerges from the self-interaction associated to the pp-waves and a self-dual condition naturally satisfied by the pp-wave scalar fields