Related papers: A brief note on how Einstein's general relativity …
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…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
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…
This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the…
Physics was in crisis at the beginning of the twentieth century because the newborn Maxwell's electromagnetism defied mechanistic preconceptions. Albert Einstein understood that the solution to the crisis required an audacious reworking of…
Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of…
It is well known that Einstein's General Relativity (GR) achieved a great success and overcame lots of experimental tests. On the other hand, GR also showed some shortcomings and flaws which today advise theorists to ask if it is the…
This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…
The objective of this paper is not simply to present an historical overview of Einstein's cosmological considerations, but to discuss the central role they played in shaping the paradigm of relativistic cosmology. This, we'll show, was a…
In this paper we review the derivation of light bending obtained before the discovery of General Relativity (GR). It is intended for students learning GR or specialist that will find new lights and connexions on these historic derivations.…
A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a…
This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, E\"otv\"os experiment, Newcomb's…
We suggest that not only quanta may have played a role in Einstein's ideas on relativity, but that they themselves may be related to the dynamical and relativistic behaviour of the electromagnetic field exhibited in a Poincar\'e's 1900…
Einstein's dream of describing elementary particles as solutions of a classical field theory is severely limited by our current understanding of Nature. Quantum theory is inconsistent with any local realistic theory such as evolving…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
Up to now, Einstein's general theory of relativity has passed all experimental tests. But yet we know that it is not a fundamental theory and that it is incompatible with quantum theory. While several extended and improved gravitational…
This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This…
I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…