Related papers: Einstein's Special Relativity: The Hyperbolic Geom…
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We give a critical analysis of the conceptual foundations of special relativity. We formulate a simple operational criterion for distinguishing between noninertial and inertial frames which is introduced prior to geometry. We associate the…
In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
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…
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 propose a new point of view for interpreting Newton's and Einstein's theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
Einstein identified singularities in spacetimes, such as at the Schwarzschild radius, where later relativists only find a coordinate system assigning multiple values to a single spacetime event. These differing judgments derive from…
We note that Einstein's relativistic Doppler formula presents a strange aspect. For incident light received under a fixed non zero angle, the Doppler shift will change from blueshift to redshift (or vice-versa) for some critical relative…
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…
The complex relationship between Einstein's second postulate and the Maxwell electromagnetic theory is elucidated. A simple deduction of the main results of the Ignatowski approach to the theory of relativity is given. The peculiar status…
The extention of the integrable ansatz of pure Einstein gravity to supergravity is completed. The procedure of construction the exact supergravitational solitonic solutions is described.
We review the special theory of relativity kinematics and dynamics as well as the general theory of relativity under the aspect of logic.
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Five topics: A rigid body does not exist in the special theory of relativity; distant simultaneity defined with respect to a given frame of reference without any reference to synchronized clocks; challenges on Einstein's connection of…
According to a simple model of inertia a Machianized theory of special and general relativity named as relational relativity is presented.
General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents,…
We propose a new model which describes relativistic hydrodynamics and generalizes the standard Euler system of isentropic perfect fluids. Remarkably, our system admits a convex extension which allows us to transform it to a symmetric…