We give a reformulation of non-linear Einstein gravity, which contains the dual graviton together with the ordinary metric and a shift gauge field. The metric does not enter through a ‘kinetic’ Einstein-Hilbert term, but via topological couplings, and so the theory does not lead to a doubling of degrees of freedom. The field equations take the form of first-order duality relations. We analyze t...

Extended Einstein-Maxwell model and its application to the problem of evolution of magnetized Bianchi-I Universe are considered. The evolution of medium magnetization is governed by a relaxation type extended constitutive equation. The series of exact solutions to the extended master equations is obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is shown to become non-...

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also...

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subj...

The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, nonlinearities correspond to convolution that numerically might lead aliasing instabilities. We present study this problem, in vacuum conditions, based on the $3+1$ Baumgarte-Shibata-Shapiro-Nakamura (BSSN)...

A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.

The Einstein–Klein–Gordon field equations are solved in a inhomogeneous shear–free universe containing a material fluid, a self–interacting scalar field, a variable cosmological term, and a heat flux. A quintessence– dominated scenario arises with a power–law accelerated expansion compatible with the currently observed homogeneous universe.

The Kähler metric which has been constructed by present author in [1] is used in this paper to find an exact solution of Einstein equations with energy-momentum tensor of special type. That type of Tij admits in particular to use it as energy-momentum tensor of charged scalar field and in case of such system the field function is determined.