Related papers: The extended Conformal Einstein field equations wi…
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as…
As is well known, both Weyl and Weitzenb\"ock spacetimes were initially used as attempts to geometrize the electromagnetic field. In this letter, we prove that this field can also be regarded as a geometrical quantity in an extended version…
Einstein's theory of general relativity is written in terms of the variables obtained from a conformal--traceless decomposition of the spatial metric and extrinsic curvature. The determinant of the conformal metric is not restricted, so the…
We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
Necessary and sufficient conditions for a space-time to be conformal to an Einstein space-time are interpreted in terms of curvature restrictions for the corresponding Cartan conformal connection.
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined…
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the…
In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly…
We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We…
Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…