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The goal of this lecture is to introduce the student to the theory of Special Relativity. Not to overload the content with mathematics, the author will stick to the simplest cases; in particular only reference frames using Cartesian…
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
In this work we consider gravitational theories in which the effect of coupling characteristic classes, appropriately introduced as operators in the Einstein-Hilbert action, has been taken into account. As it is well known, this approach…
Many different families of mass models are used in modern applications of strong gravitational lensing. I review a wide range of popular models, with two points of emphasis: (1) a discussion of strategies for building models suited to a…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
We review the foundations of Einstein's general theory of relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for new generation of high-accuracy gravitational experiments. We discuss the…
Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
The Einstein Toolkit represents a unique opportunity for students to explore the world of numerical relativity, without the need for high-level computing power or knowledge of the mathematics behind the simulations themselves. This document…
General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the…
In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
The main interest of the work exposed in this thesis is to explore hairy black holes in a more general framework than General Relativity by taking into account the presence of a cosmological constant, of higher dimensions, of exotic matter…