Related papers: Averaging in LRS class II spacetimes
For the non-tachyonic curvature squared action we show that the expanding Bianchi-type I models tend to the dust-filled Einstein-de Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period.…
The tree-level scattering amplitudes of general relativity encode the full non-linearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative…
The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a…
The current cosmological model ($\Lambda$CDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average…
In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a…
This thesis is a review of backreaction, which is a possible alternative to dark energy and modified gravity. We describe in detail the 3+1 covariant formalism and Frobenius' theorem. We present the averaging procedure developed by Buchert,…
One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root…
We discuss the Buchert equations, which describe the average expansion of an inhomogeneous dust universe. In the limit of small perturbations, they reduce to the Friedmann-Robertson-Walker equations. However, when the universe is very…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
In this paper we consider the relation between the volume deceleration parameter obtained within the Buchert averaging scheme and the deceleration parameter derived from the supernova observation. This work was motivated by recent findings…
After a concise overview of Einstein spacetimes of type II (or more special) in four and five dimensions, we summarize recent results in the six-dimensional case. We assume the optical matrix to be non-degenerate and ``generic'', and the…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
Recently it was established in Einstein-Maxwell-Dilaton gravity that the KSS viscosity/entropy ratio associated with AdS planar black holes can be viewed as the boundary dual to the generalized Smarr relation of the black holes in the bulk.…
The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. The non-linearity of the Einstein field equations raises concern over…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly…