Related papers: Symmetry reduced Einstein gravity and generalized …
We study the two-dimensional (2D) dilatonic model describing a massless scalar field minimally coupled to the spherically reduced Einstein-Hilbert gravity. The general solution of this model is given in the case when a Killing vector is…
We present a class of numerical solutions to the SU(2) nonlinear $\sigma$-model coupled to the Einstein equations with cosmological constant $\Lambda\geq 0$ in spherical symmetry. These solutions are characterized by the presence of a…
We consider a class of ans\"atze for the construction of exact solutions of the Einstein-nonlinear $\sigma$-model system with an arbitrary cosmological constant in (3+1) dimensions. Exploiting a geometric interplay between the $SU(2)$ field…
Almost a century ago, Einstein used a weak field approximation around Minkowski space-time to calculate the energy carried away by gravitational waves emitted by a time changing mass-quadrupole. However, by now there is strong observational…
We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
We construct a Lagrangian of Weyl spinors and gauge fields, which is invariant under the action of equivalent local transformations on the spinor algebra representations. A model of vacuum with a nontrivial gauge strength-tensor setting a…
We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern-Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
We propose novel asymptotically locally flat boundary conditions for Einstein Gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are…
Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or…
The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this…
Spherical reduction of generic four-dimensional theories is revisited. Three different notions of "spherical symmetry" are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and…
The approach, referred to as "monodromy transform", provides some general base for solution of all known integrable space - time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of…
Algebraically general para-K\"ahler Einstein spaces equipped with 3D algebras of infinitesimal symmetries are considered. It is shown that if the algebra contains 2D trivial subalgebra then vacuum Einstein field equations with cosmological…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…