Related papers: Solving gravitational field equations by Wiener-Ho…
We search a gravitational system which allows a non-relativistic hybrid geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution, as a continuation of the previous work employing a flow equation. As such a candidate an…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…
We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
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…
For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the…
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar…
We investigate two-dimensional higher derivative gravitational theories in a Riemann-Cartan framework and obtain the most general static black hole solutions in conformal coordinates. We also consider the hamiltonian formulation of the…
This thesis focuses on the application of numerical relativity methods to the solutions of problems in strong gravity. Our goal is the study of mergers of compact objects in the strong field regime where non-linear dynamics manifest and…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based…
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…
We study a Born-Infeld inspired model of gravity and electromagnetism in which both types of fields are treated on an equal footing via a determinantal approach in a metric-affine formulation. Though this formulation is a priori in conflict…
We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of…
Quantum theory of conformal factor coupled with matter fields is investigated. The more simple case of the purely classical scalar matter is considered. It is calculated the conformal factor contribution to the effective potential of scalar…
We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field…
We study geodesic equations for a family of right-invariant Riemannian metrics on the group of diffeomorphisms of a compact manifold. The metrics descend to Fisher's information metric on the space of smooth probability densities. The right…