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Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
The initial singularity problem in standard general relativity is treated on the light of a viewpoint asserting that this formulation of Einstein's theory and its conformal formulations are physically equivalent. We show that flat…
The conformal transformation in the Einstein - Hilbert action leads to a new frame where an extra scalar degree of freedom is compensated by the local conformal-like symmetry. We write down a most general action resulting from such…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
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…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
A novel approach to quantization is shown to allow for superpositions of the cosmological constant in isotropic and homogeneous mini-superspace models. Generic solutions featuring such superpositions display unitary evolution and resolution…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
A new canonical transformation is found that enables the direct canonical treatment of the conformal factor in general relativity. The resulting formulation significantly simplifies the previously presented conformal geometrodynamics. It…
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 consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the…
This article gives a review of a recent construction, the ambient cosmological metric, and its implications for the global geometry of the universe. According to this proposal, the universe is a bounding hypersurface carrying a conformal…
We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…