Related papers: The not-so-nonlinear nonlinearity of Einstein's eq…
We introduce a simple and straight-forward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously…
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…
Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of…
The second order perturbations in Friedmann-Robertson-Walker universe filled with a perfect fluid are completely formulated in the gauge invariant manner without any gauge fixing. All components of the Einstein equations are derived…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
We show that the relativistic effects are negligibly small in the non-linear density and velocity bispectra. Although the non-linearities of Einstein equation introduce additional non-linear terms to the Newtonian fluid equations, the…
We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically…
A rigorous quantum relativistic approach has been used to calculate the relationship between the decay laws of an unstable particle seen from two inertial frames moving with respect to each other. In agreement with experiment, it is found…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
In a nonlinear theory, such as gravity, physically relevant solutions are usually hard to find. Therefore, starting from a background exact solution with symmetries, one uses the perturbation theory, which albeit approximately, provides a…
We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…
By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of…