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The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We present the theory of special relativity here through the lens of differential geometry. In particular, we explicitly avoid any reference to hypotheses of the form "The laws of physics take the same form in all inertial reference frames"…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
In his 1916 ground-breaking general relativity paper Einstein had imposed a restrictive coordinate condition, his field equations were valid for coordinate systems which are unimodular. Later, Einstein published a paper on gravitational…
I reconsider Einstein's 1912 "Prague-Theory" of static gravity based on a scalar field obeying a non-linear field equation. I point out that this equation follows from the self-consistent implementation of the principle that all energies…
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…
Chae's analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein's general relativity, the…
Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
The mantra about gravitation as curvature is a misnomer. The curvature tensor for a standard of rest does not describe acceleration in a gravitational field but the \underline{gradient} of the acceleration (e.g. geodesic deviation). The…
The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…
We propose an action-based $ f(R) $ modification of Einstein's gravity which admits of a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the newtonian potential. A…
Albert Einstein's journey to formulate the theory of general relativity involved significant shifts in his approach to gravitational field equations. Starting in 1912, he collaborated with Marcel Grossmann and initially explored broadly…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
We analyse a generalisation of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum, $c,$ and the Newtonian gravitation 'constant', $G,$ proposed by Albrecht and Maguejo. We find exact solutions…