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The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using General Relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
We use the gravitoelectromagnetic approach to the solutions of Einstein's equations in the weak-field and slow-motion approximation to investigate the impact of General Relativity on galactic dynamics. In particular, we focus on a class of…
Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We consider the unification problem for the gravitational and electromagnetic interactions and its possible solution on the basis of the existence of an effective Riemannian space in nonlinear electrodynamics
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…
It is a well known fact that, in the absence of Dark Matter, the observation of the rotation curves of galaxies cannot be explained in terms of Newtonian gravity. Rotation curves become flat in the outer regions, in contrast to what is…
An overview of the experimental and observational status in gravitational physics is given, both for the known tests of general relativity and Newtonian gravity, but also for the increasing number of results where these theories run into…
Relativistically covariant form of equation of motion for real particle (neutral in charge) under the action of electromagnetic radiation is derived. Various formulations of the equation of motion in the proper frame of reference of the…
We study a generalized Einstein theory with the following two criteria:{\it i}) on the solar scale, it must be consistent with the classical tests of general relativity, {\it ii}) on the galactic scale, the gravitational potential is a sum…
Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional…
In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications…
Relativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin…
The post-Newtonian approximation is a method for solving Einstein's field equations for physical systems in which motions are slow compared to the speed of light and where gravitational fields are weak. Yet it has proven to be remarkably…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…