Related papers: Vacuum Einstein metrics with bidimensional Killing…
It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find…
We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally K\"ahler…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
The paper develops a $(2+2)$-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The formalism is two-dimensionally covariant, and leads to simple, geometrically…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
We study the existence of projectable $G$-invariant Einstein metrics on the total space of $G$-equivariant fibrations $M=G/L\to G/K$, for a compact connected semisimple Lie group $G$. We obtain necessary conditions for the existence of such…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
We obtain a dynamical formulation of two-dimensional gravity from a non-Einsteinian phase in higher dimensions $(D=3+2n)$. The formalism is associated with (at least) one extra dimension of vanishing proper length, thus being inequivalent…
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…
Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex…