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We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing 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…
An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give various characterizations of scalar curvature rigidity for…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
We investigate the possibility that the conformal and conformal thin sandwich (CTS) methods can be used to parameterize the set of solutions of the vacuum Einstein constraint equations. To this end we develop a model problem obtained by…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
We give some uniform estimates for constant mean curvature solutions of the conformal vacuum Einstein constraint equations on compact manifolds. Existence of those solutions was given in a paper by J. Isenberg.
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…
The conformal formulation provides a method for constructing and parametrizing solutions of the Einstein constraint equations by mapping freely chosen sets of conformal data to solutions, provided a certain set of coupled, elliptic…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is…
We present a uniform (and unambiguous) procedure for scaling the matter fields in implementing the conformal method to parameterize and construct solutions of Einstein constraint equations with coupled matter sources. The approach is based…
A closed explicit representation of the vacuum Einstein equations in terms of components of curvature 2-forms is given. The discussion is restricted to the case of non-vanishing cubic invariant of conformal curvature spinor. The complete…
We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…