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The article is a natural continuation of the papers by Gavrilov and Gitman (Class.Quant.Grav. {\bf 17} (2000) L133; Int. J. Mod. Phys. A15 (2000) 4499) devoted to relativistic particle quantization. Here we generalize the problem,…
We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge…
Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon as interactions with gravity are…
A new idea of quantum gravity is developed based on {\it Gravitational Complementary Principle}. This principle states that gravity has dual complement features: The quantum and classical aspects of gravity are complement and absolutely…
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 space expansion physics contains several paradoxes which were clearly demonstrated by Edward Harrison (1981, 1995, 2000), who emphasized that the cooling of homogeneous hot gas (including photon gas of CBR) in the standard cosmological…
This thesis is situated within the context of quantum gravity, broadly understood as any effort to explore the interplay between gravitation and the quantum realm, without necessarily requiring the quantization of the gravitational field…
In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak…
Perturbative techniques are important for modified theories of gravity since they allow to calculate deviations from General Relativity without recurring to exact solutions, which can be difficult to find. When applied to models such as…
Searches for empirical clues beyond Einstein's general relativity (GR) are crucial to understand gravitation and spacetime. Radio pulsars have been playing an important role in testing gravity theories since 1970s. Because radio timing of…
The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General…
Recent astronomical observations verify the new scenario resulting from new conservation laws and a new relativity principle fixed either by dual properties of light or by new gravitational (G) tests and the Einstein's equivalence…
General Relativity (GR) is consistent with a wide range of experiments/observations from millimeter scales up to galactic scales and beyond. However, there are reasons to believe that GR may need to be modified because it includes…
It is first argued that radiation by a uniformly accelerated charge in flat space-time indicates the need for a unified geometric theory of gravity and electromagnetism. Such a theory, based on a metric-affine $U_4$ manifold, is constructed…
The bimetric theory of gravity is an extension of general relativity that describes a massive spin-$2$ particle in addition to the standard massless graviton. The theory is based on two dynamical metric tensors with their interactions…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein's field equations, but rather to insufficiencies in the mathematics used for their…
In 1945 Einstein concluded that [1]: "The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…
The scalar-tensor theory of gravitation has been and still is one of the most widely discussed "alternative theories" to General Relativity (GR). Despite nearly half a century of its age, it continues to attract renewed interests of not…
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…