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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…
The most simple observed cases of gravitational lensing of distant quasars and galaxies by galaxies and clusters of galaxies are used to test Einstein's theory of General Relativity and Newtonian Gravity over galactic and intergalactic…
The debate on gravity theories to extend or modify General Relativity is very active today because of the issues related to ultra-violet and infra-red behavior of Einstein's theory. In the first case, we have to address the Quantum Gravity…
General relativity can be formulated either as in its original geometrical version (Einstein, 1915) or as a field theory (Feynman, 1962). In the Feynman presentation of Einstein theory an hypothesis concerning the interaction of gravity to…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this essay…
The issue of implementing the principle of general relativity in Einstein equations has been widely discussed, since Kretschmann's well-known criticism stated that general covariance of the Einstein equations is not suffice to express the…
Recent experiments have successfully tested Einstein's general theory of relativity to remarkable precision. We discuss recent progress in the tests of relativistic gravity in the solar system and present motivations for the new generation…
It is well known that Einstein's General Relativity (GR) achieved a great success and overcame lots of experimental tests. On the other hand, GR also showed some shortcomings and flaws which today advise theorists to ask if it is the…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
Equivalence principles played a central role in the development of general relativity. Furthermore, they have provided operative procedures for testing the validity of general relativity, or constraining competing theories of gravitation.…
The Einstein-Hilbert action of general theory of relativity (GR) is the integral of the scalar curvature $R$. It is a theory that is drawn from the Equivalence principle, and has predictions that come out as a consequence of the principle,…
The Equivalence Principle (EP) is not one of the ``universal'' principles of physics (like the Action Principle). It is a heuristic hypothesis which was introduced by Einstein in 1907, and used by him to construct his theory of General…
Einstein's theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical…
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…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for…
In this review we aim to describe the most stringent tests of the strong equivalence principle, the fundamental principle of General Relativity, using pulsar timing. For this purpose, we first construct the parametrized post-Newtonian and…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
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…