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We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-$2$ degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces., Comment: This version has significant improvements: causality discussion of all the well-known gravity theories in flat space is extended to the AdS space, references added, 29 pages, latest version matches the published one

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the pointwise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet, and Euler-Heisenberg. Fil: Abalos, Julio Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Carrasco, Federico León. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Goulart, Érico. CAPES Foundatio; Brasil Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina

We study circular shells in a (2+1)-dimensional background within the framework of Einstein-Born-Infeld theory. For shells around black holes we analyze the mechanical stability under perturbations preserving the symmetry. Shells around vacuum are also discussed. We find a large range in the values of the parameters compatible with stable configurations., Comment: 10 pages, 6 figures; v2: improved version, new references added

Motivated by possible applications within the framework of anti-de Sitter gravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by a nonlinear electrodynamics (NED) are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Fall-off conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures., 30 pages, no figures; a few references added; final version for PRD

We show that a class of bi-gravity theories contain solutions describing dark matter. A particular member of this class is also shown to be equivalent to the Eddington-Born-Infeld gravity, recently proposed as a candidate for dark matter. Bigravity theories also have cosmological de Sitter backgrounds and we find solutions interpolating between matter and acceleration eras., Comment: 4 pages, 1 figure, minor corrections and reference additions, published in Phys. Rev. D

The advent of explicit Dirac-Born-Infeld (DBI) inflationary models within string theory has drawn renewed interest to the cosmological role of unusual scalar field dynamics, usually referred to as k-inflation. In this situation, the standard method used to determine the behavior of cosmological perturbations breaks down. We present a generic method, based on the uniform approximation, to analytically derive the power spectra of scalar and tensor perturbations. For this purpose, a simple hierarchy of parameters, related to the sound speed of the cosmological fluctuations and its successive derivatives, is introduced in a k-inflation analogue of the Hubble flow functions. The scalar spectral index and its running are obtained up to next to next to leading order for all k-inflationary models. This result relies on the existence of a well-motivated initial state, which is not trivial in the present context: having the wavelength of the Fourier mode smaller than the sonic horizon is indeed not enough and some conditions on the dynamics of the sound speed are also required. Our method is then applied to various models encountered in the literature. After deriving a generic slow-roll trajectory valid for any DBI model, simple formulae for the cosmological observables are obtained. In particular, the running, as the spectral index, for the so-called UV and IR brane inflationary models is found to be uniquely determined by the 't Hooft coupling. Finally, the accuracy of these cosmological predictions is assessed by comparing the analytical approximations with exact numerical integrations., Comment: 21 pages, 9 figures, uses RevTeX. References added, misprints corrected, matches published version

Waveguides can be employed to test non-linear effects in electrodynamics. We solve Born-Infeld equations for TE waves in a rectangular waveguide. We show that the energy velocity acquires a dependence on the amplitude, and harmonic components appear as a consequence of the non-linear behavior., Comment: 3 pages. To appear in PRL