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The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
Long before the general theory of relativity was finally formulated in 1916, arguments based entirely on Einstein's equivalence principle predicted the well known phenomenon of the gravitational red shift. Precisely the same arguments are…
The equivalence principle was formulated by Einstein in an attempt to extend the concept of inertial frames to accelerated frames, thereby bringing in gravity. In recent decades, it has been realised that gravity is linked not only with…
The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match…
The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
Einstein's explanation of Mercury's perihelion motion has been verified by astronomical observations. His formula could also be obtained in Schwarzschild metric and was published already in 1898. Motion along a straight geodesic, however,…
Suggested theory involves a drastic revision of a role of local internal symmetries in physical concept of curved geometry. Under the reflection of fields and their dynamics from Minkowski to Riemannian space a standard gauge principle of…
There have been various claims that the Equivalence Principle, as originally formulated by Einstein, presents several difficulties when extended to the quantum domain, even in the regime of weak gravity. Here we point out that by following…
Einstein action of gravity is obtained from a gauge theory, if our spacetime was once in two folds with a double Lorentz symmetry. After the dual symmetry breaks spontaneously, Lorentz symmetry absorbs gauge symmetry, while the gauge field…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
General relativity and quantum mechanics are perhaps the two most successful theories of the XXth century. Despite their impressive accurate predictions, they are both valid at their own scales and do not seem to be expressible using the…
Einstein said that gravity is an acceleration like any other acceleration. But gravity causes relativistic effects at non-relativistic speeds; so gravity could have relativistic origins. And since the strong force is thought to cause most…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the…
Between 1905 and 1907, Einstein first tried to extend the special theory of relativity in such a way so as to explain gravitational phenomena. This was the most natural and simplest path to be taken. These investigations did not fit in with…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…