Related papers: Mathematical Features of Several Cosmological Mode…
We suggest an interpretation of Einstein Equations of General Relativity at large scales in which the Cosmological constant is exactly zero in the limit of zero spacetime variations of fundamental constants. We argue that in a…
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
Considering the physical 3-space t = constant of the spacetime metrics as spheroidal and pseudo spheroidal, cosmological models which are generalizations of Robertson-Walker models are obtained. Specific forms of these general models as…
We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein-Friedmann equations. These analogies produce an effective Lagrangian and…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
We consider numerically dynamics of a flat anisotropic Universe in Einstein-Gauss-Bonnet gravity with positive $\Lambda$ in dimensionalities 5+1 and 6+1. We identify three possible outcomes of the evolution, one singular and two…
The spatially homogeneous, isotropic Standard Cosmological Model appears to describe our Universe reasonably well. However, Einstein's equations allow a much larger class of cosmological solutions. Theorems originally due to Penrose and…
The problem of possible astrophysical consequences of the existence of exotic differential structures on manifolds is discussed. It is argued that corrections to the curvature of the form of a source like terms should be expected in the…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's…
In view of late-time cosmic acceleration, a dark energy cosmological model is revisited wherein Einstein's cosmological constant is considered as a candidate of dark energy. Exact solution of Einstein field equations (EFEs) is derived in a…
First the second-order perturbations of nonzero-\Lambda cosmological models are derived with an arbitrary potential function of spatial coordinates, using the nonlinear version of Lifshitz's method in the synchronous gauge. Their expression…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
We study here some consequences of the nonlinearities of the electromagnetic field acting as a source of Einstein's equations on the propagation of photons. We restrict to the particular case of a ``regular black hole'', and show that there…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…
We give an overview of progress on homogeneous Einstein metrics on large classes of homogeneous manifolds, such as generalized flag manifolds and Stiefel manifolds. The main difference between these two classes of homogeneous spaces is that…
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If $M$ is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein…