Related papers: Self-Similarity in General Relativity \endtitle
Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The…
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
Spherically symmetric solutions admitting a homothetic Killing vector field (HKVF) either orthogonal, $\eta_{\bot}$, or parallel,$\eta_{||}$, to the 4-velocity vector field, $u^a$, are studied. New self-similar solution of Einstein's field…
We consider homogeneous and isotropic cosmological models in the framework of three geometrical theories of gravitation: in the Einstein general relativity they are given in terms of the curvature of the Levi-Civita connection in torsion…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible…
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
Spherically symmetric solutions in F(R) theories in astronomical systems with rising energy density are studied. The range of parameters is established for which the flat space-time approximation for the background metric is valid. For the…
We study a theory of gravity of the form $f(\mathcal{G})$ where $\mathcal{G}$ is the Gauss-Bonnet topological invariant without considering the standard Einstein-Hilbert term as common in the literature, in arbitrary $(d+1)$ dimensions. The…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable…
In this paper we provide a classification of plane symmetric kinematic self-similar perfect fluid and dust solutions. In the perfect fluid and dust cases, kinematic self-similar vectors for the tilted, orthogonal and parallel cases have…
[Abridged] If gravitation is to be described by a hybrid metric-Palatini $f(\mathcal{R})$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow…
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the…
In this manuscript we investigate the intrinsically flat (space-flat) spacetimes as viable cosmological models. We show that they have a natural geometric structure which is suitable to describe inhomogeneous matter distributions forming a…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…
We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…