Related papers: A technique for generating new solutions of Einste…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical…
We present a non-isospectral GBDT version of B\"acklund-Darboux transformation for the gravitational and $\sigma$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix…
We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
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 new regular solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by a pair of integers (k,n), where k is related to the polar angle and $n$ to the azimuthal…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in [15, 16, 24], namely existence when the so called TT-tensor…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…
Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact…
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and…
We consider an extended version of the Kerr theorem incorporated in the Kerr-Schild formalism. It allows one to construct the series of exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
In this letter we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of…
The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the…
We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their…
In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling…
For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…