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The TOV equation appears as the relativistic counterpart of the classical condition for hydrostatic equilibrium. In the present work we aim at showing that a generalised TOV equation also characterises the equilibrium of models endowed with other symmetries besides spherical. We apply the dual null formalism to spacetimes with two dimensional spherical, planar and hyperbolic symmetries with a perfect fluid as the source. We also assume a Killing vector field orthogonal to the surfaces of symmetry, which gives us static solutions, in the timelike Killing field case, and homogeneous dynamical solutions in the case the Killing field is spacelike. In order to treat equally all the aforementioned cases, we discuss the definition of a quasi-local energy for the spacetimes with planar and hyperbolic foliations, since the Hawking-Hayward definition only applies to compact foliations. After this procedure, we are able to translate our geometrical formalism to the fluid dynamics language in a unified way, to find the generalized TOV equation, for the three cases when the solution is static, and to obtain the evolution equation, for the homogeneous spacetime cases. Remarkably, we show that the static solutions which are not spherically symmetric violate the weak energy condition (WEC). We have also shown that the counterpart of the TOV equation for the spatially homogeneous models is just the familiar equation \r{ho} + P = 0, defining a cosmological constant-type behaviour, both in the hyperbolic and spherical cases. This implies a violation of the strong energy condition in both cases, added to the above mentioned violation of the weak energy condition in the hyperbolic case. We illustrate our unified treatment obtaining analogs of Schwarzschild interior solution, for an incompressible fluid $\rho = \rho_0$ constant., Comment: 10 pp, 1 fig

In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant., Comment: 45 pages, 11 figures

New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided., Latex, 27 pages plus 16 figures (not included, available from the authors upon request) DFFCUL-94-01-01

A class of orthogonal, spatially homogeneous shear-free cosmological models with an imperfect liquid matter content is considered. It is shown that, for these models, the anisotropic stresses are related to the anisotropic curvature of the spatial hypersurfaces through the electric part of the Weyl tensor. This creates a counterbalance effect which has important consequences for the evolution of the cosmological models. Such features are discussed, and, as an application, some eternally anisotropic models with an imperfect fluid stress tensor which exhibit FRW-like behaviour are given.

We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical fluids} that differ in meaning with respect to the matter fluids generally considered as sources of the field equations. In extended gravity theories the curvature terms are encapsulated in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$ that can be recast as effective Einstein field equations, with corrections to the energy-momentum tensor of matter. The formal validity of standard energy inequalities does not assure basic requirements such as the attractive nature of gravity, so we argue that the energy conditions have to be considered in a wider sense., Comment: Sumbitted to the Proceedings of the Spanish Relativity Meeting- ERE2014"Amost 100 years after Einstein revolution", to appear in the Journal of Physics: Conference Series

Motivated by string/M-theory predictions that scalar field couplings with the Gauss-Bonnet invariant, G, are essential in the appearance of non-singular early time cosmologies, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity, and present the viability bounds arising from the energy conditions. In particular, we consider a specific realistic form of f(G) analyzed in the literature that accounts for the late-time cosmic acceleration and that has been found to cure the finite-time future singularities present in the dark energy models, and further examine the respective viability of the specific f(G) model imposed by the weak energy condition., 4 pages. Prepared for the proceedings of the Spanish Relativity meeting (ERE2010), Granada, Spain, 6-10 Sep 2010

We present a mechanism that generates the exact solutions of scalar field cosmologies in an unified way. This applies both to standard and phantom scalar fields in the framework of Einsteins General Relativity, and also to extended scenarios based on generalized gravity theories such as Scalar-Tensor theories. We provide a classification of the solutions in terms a single generating function. The existence of form-invariant dualities between the solutions is also discussed.

We investigate cosmological dynamics of models with higher-order corrections to the canonical (second-order) kinetic lagrangian for a scalar field, which have been termed k-essence. We study the qualitative dynamics of simple purely kinetic k-essence models and find that the simplest attempts to construct non-singular cosmological models by including higher-order terms in the kinetic lagrangian fail because of a di.erent type of singularity where the scalar field theory becomes ill-defined.