Related papers: Self-dual Einstein spaces and the general heavenly…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
The evolution of self-gravitating collision-less matter and scalar waves within the general relativity context is described by Einstein and Vlasov equations. The sources of Einstein equations are generated by a distribution function and a…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use…
The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
The reduction of 4D Einstein gravity with $N$ minimal scalars leads to specific 2D dilaton gravity with dilaton coupled scalars. Applying s-wave and large $N$ approximation (where large $N$ quantum contribution due to dilaton itself is…
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the…
It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact…
The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the…
We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation, both allowing for arbitrary dimensionality, and non-linearity. For one of these generalisations, we characterise all solutions…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries…
Reconsidering the harmonic space description of the self-dual Einstein equations, we streamline the proof that all self-dual pure gravitational fields allow a local description in terms of an unconstrained analytic prepotential in harmonic…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant $\Lambda$ equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always…
The Newman-Penrose map, which is closely related to the classical double copy, associates certain exact solutions of Einstein's equations with self-dual solutions of the vacuum Maxwell equations. Here we initiate an extension of the…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…