Related papers: The General Solution of Bianchi Type $VII_h$ Vacuu…
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to…
We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
We construct a new family of exact vacuum black brane solutions to five-dimensional Einstein gravity with a negative cosmological constant, characterized by a homogeneous horizon with Bianchi VI$_h$ symmetry. This construction generalizes…
Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution.…
We construct new classes of cosmological solution to the five dimensional Einstein-Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional…
In this work we compile a few differential equations (ODEs) that arise from the relativistic equations in cosmological models that consider the ``constants'' as scalars functions dependent on time and they are described as perfect as well…
The general exact solution of the Einstein-Dirac equations with cosmological constant in the homogeneous Riemannian space of the Bianchi 1 type is obtained.
The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological…
Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented, together…
Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher…
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be non-separable functions of time and the extra coordinate $l$ and the induced metric on $l$ = constant…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
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 introduce two new families of solutions to the vacuum Einstein equations with negative cosmological constant in 5 dimensions. These solutions are static black holes whose horizons are modelled on the 3-geometries nilgeometry and…
We investigate the set of spacetime general coordinate transformations (G.C.T.) which leave the line element of a generic Bianchi Type Geometry, quasi-form invariant; i.e. preserve manifest spatial Homogeneity. We find that these G.C.T.'s,…
In this work, we will explore the effects of F(R) theories in the classical scheme using the anisotropic Bianchi Type I cosmological model with standard matter employing a barotropic fluid with equation of state $P=\gamma \rho$. In this…
Orientifold solutions have an unphysical region around their source; for the O6, the singularity is resolved in M-theory by the Atiyah-Hitchin metric. Massive IIA, however, does not admit an eleven-dimensional lift, and one wonders what…