Related papers: Special Relativity, Einstein Velocity Addition, an…
As is well-known, Newton's gravitational theory can be formulated as a four-dimensional space-time theory and follows as singular limit from Einstein's theory, if the velocity of light tends to the infinity. Here 'singular' stands for the…
There have been a number of papers proposing that the light speed of a homogeneous and isotropic universe is variable. This paper outlines a simple way that the vectors and tensors of special relativity can be extended to allow such a…
The decomposition $\Gamma=BH$ of a group $\Gamma$ into a subset $B$ and a subgroup $H$ of $\Gamma$ induces, under general conditions, a group-like structure for $B$, known as a gyrogroup. The famous concrete realization of a gyrogroup,…
The theory of special relativity can be generalized by means of a new principle called Conservation of Information. This allows a derivation of the constancy of the velocity of light with respect to moving frames, and, consequently, of…
The aim of this work is to show, on the example of the behaviour of the spinless charged particle in the homogeneous electric field, that one can quantized the velocity of particle by the special gauge fixation. The work gives also the some…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing…
These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
It has been almost one hundred years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space-time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations…
Starting from the weak field limit, we discuss astrophysical applications of Extended Theories of Gravity where higher order curvature invariants and scalar fields are considered by generalizing the Hilbert-Einstein action linear in the…
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or…
These notes give a concise introduction to General Relativity at the advanced undergraduate level, starting from the weak field limit and gravitational waves, then introducing curved manifolds and Riemannian geometry. The nonlinear…
There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…
We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
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…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a…
Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two…