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After recalling the conceptual foundations and the basic structure of general relativity, we review some of its main modern developments (apart from cosmology) : (i) the post-Newtonian limit and weak-field tests in the solar system, (ii)…
On incorporating special relativity theory into an extended equivalence principle, post-Newtonian gravitational phenomena beyond that originally predicted by Einstein are predicted (required), such as geodetic and gravitomagnetic…
Observations provide increasingly strong evidence that the universe is accelerating. This revolutionary advance in cosmological observations confronts theoretical cosmology with a tremendous challenge, which it has so far failed to meet.…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
This remodeled form of Einstein's relativity theories retains and incorporates only experimentally proven principles. It is based on a generalized law for spinning and rotational motions, which is in fact the conservation law of momentum…
The crucial role played by pressure in general relativity is explored in the mathematically simple context of a static spherically symmetric geometry. By keeping all pressure terms, the standard formalisms of rotation curve and…
General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents,…
Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
We present a theory of modified gravity, inspired by the gauge theories, where the commutator algebra of covariant derivative gives us an added term with respect to the General Relativity, which represents the interaction of gravity with a…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
Standard General Relativity assumes that, in the absence of classical matter sources, spacetime is empty. This chapter considers and analyses the new behaviours of the gravitational field that appear when one substitutes this emptiness by a…
The late-time cosmic acceleration may be due to infra-red modifications of General Relativity. In particular, we consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. Generally,…
A new form of the dynamical equations of vacuum general relativity is proposed. This form involves the canonical Hamiltonian structure but non canonical variables. The new field variables are the electric field $E^{a}{}_{i}$ and the…
In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is…
The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of…