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We develop a geometric and explicit construction principle that generates classes of Poincare-Einstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition;…
We consider the problem of building inhomogeneous cosmological models in scalar-tensor theories of gravity. This starts by splitting the field equations of these theories into constraint and evolution equations, and then proceeds by…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some…
The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled…
This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
The Kasner metrics are among the simplest solutions of the vacuum Einstein equations, and we use them here to examine the conformal method of finding solutions of the Einstein constraint equations. After describing the conformal method's…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
This paper is devoted to the study of the constraint equations of the Lovelock gravity theories. In the case of an empty, compact, conformally flat, time-symmetric, and space-like manifold, we show that the Hamiltonian constraint equation…
Our paper introduces a new theoretical framework called the Fractional Einstein--Gauss--Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we…
Standard methods in non-linear analysis are used to show that there exists a parabolic branching of solutions of the Lichnerowicz-York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
The purpose of this work is to discuss how matter fields are coupled to gravity within the framework of General Relativity. Our particular focus here is on the coupling of scalar field models. In a first step, we suggest a new method for…
We find the conditions under which scale-invariant Einstein-Cartan gravity with scalar matter fields leads to an approximate conformal invariance of the flat space particle theory up to energies of the order of the Planck mass. In the…
We propose an Einstein-{\ae}ther scalar-tensor cosmological model. In particular in the scalar-tensor Action Integral we introduce the {\ae}ther field with {\ae}ther coefficients to be functions of the scalar field. This cosmological model…
Theoretical arguments and cosmological observations suggest that Einstein's theory of general relativity needs to be modified at high energies. One of the best motivated higher-curvature extensions of general relativity is…