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Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture}…
We present the second-order gravitational dynamics for a spacetime inhabited by matter fields which feature vacuum birefringence. The derivation follows a perturbative variant of the covariant constructive gravity program, ensuring…
We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat…
We give a new definition, based on considerations of well-posedness for a certain asymptotic initial value problem, of the phase space for the radiative degrees of freedom of the gravitational field in exact General Relativity. This space…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
We analyze the dispersion relation for an anisotropic gravity-electromagnetic theory at very high energies. In particular for photons of very high energy. We start by introducing the anisotropic gravity-gauge vector field model. It is…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal…
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…
We study the classical and quantum dynamics of generally covariant theories with vanishing a Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution…
In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between…
The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the…
In 'modified' gravity the observed acceleration of the universe is explained by changing the gravitational force law or the number of degrees of freedom in the gravitational sector. Both possibilities can be tested by measurements of…
In Part I of this series, the author has shown how to extend the framework of Riemannian geometry so as to include infinitesimals of higher than first order. The purpose of the present contribution is to initiate an investigation into the…