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General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
A scalar-tensor theory of gravity is formulated in which $G$ and particle masses are allowed to vary. The theory yields a globally static cosmological model with no evolutionary timescales, no cosmological coincidences, and no flatness and…
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and…
I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a…
In this paper are discussed possible many body generalizations of the expanding locally anisotropic metric ansatz with respect to approximately Newtonian gravitational systems. This ansatz consistently describes local point-like matter…
Dark matter is estimated to make up ~84% of all normal/baryonic matter, but cannot be directly imaged. Despite the fact that dark matter cannot be directly observed yet, its influence on the motion of stars and gas in spiral galaxies have…
In this article we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian…
There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe…
We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in…
The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
We derive the radial acceleration of stars in galaxies by using basic features of thermodynamics, statistical mechanics and general relativity. We assume that the "dark" component of the radial acceleration is originated from the reaction…
We analyse the Einstein-Cartan gravity in its standard form cal-R = R + cal-K^2, where cal-R and R are the Ricci scalar curvatures in the Einstein-Cartan and Einstein gravity, respectively, and cal-K^2 is the quadratic contribution of…
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…
We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive…
The existence of "dark matter", inferred from the observed rotation curves of galaxies, is a hypothesis which is widely regarded as problematic. This paper proposes an alternative hypothesis based on the space-time geometry near a rotating…
Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular…
Two forms are suggested for the energy-momentum source term associated with an aggregate of dark matter (with the properties described in Paper I). Both have large pressure-like components which dominate the density terms. Using one form a…