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Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined…
On the basis of his `Z\"urich Notebook' I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this…
We postulate that all the presently known kinematic effects on physical quantities related to a material particle (e.g., masss increase) are due to its velocity relative to surrounding matter, and not to the observer's reference frame. The…
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 present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Gravitational lensing - the deflection of light rays by gravitating matter - has become a major tool in the armoury of the modern cosmologist. Proposed nearly a hundred years ago as a key feature of Einstein's theory of General Relativity,…
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…
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…
According to Einstein, the trajectory of a particle that is predicted by special relativistic mechanics is well approximated by the trajectory predicted by Newtonian mechanics if the particle speed is low, i.e., much less than the speed of…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This generalization also follows by restricting variations of the…
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is…
Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…
The constancy of the speed of light (the maximum velocity of interaction) is the second postulate of Albert Einstein's special theory of relativity. Currently, there is no correct theoretical proof of this constancy in all inertial frames…
We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit…
Had Einstein followed the Bianchi differential identity for the derivation of his equation of motion for gravitation, $\Lambda$ would have emerged as a true new constant of spacetime on the same footing as the velocity of light? It is then…