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It is emphasized that antigravity (an effective repulsion of antiparticles) is a consequence of gravity invariance relative to the time reversal T. This allows one to distinguish true elementary particles from antiparticles among mesons. Attention is given to a possible violation of T-symmetry and parity non-conservation in gravitational interactions. This makes a search for antigravity a paramount task.

Based upon the results of gravitational experiments with atomic clocks, it is proved that general relativity is incompatible with quantum mechanics.

Attention is given to serious difficulties of general relativity conditioned by the ascription of the role of gravitational charge to energy. It is emphasized again that the formula for energy obtained on the basis of Minkowski's equation (for the contravariant 4-vector of energy-momentum) describes a gravitational repulsion.

According to general relativity gravitation effects any objects carrying the energy. Therefore, virtual photons (as real ones) and gravitons (real and virtual) must be attracted by massive bodies. As a result, black holes must not radiate gravitational waves and appear to be electrically and gravitationally neutral.

Antiparticles are particles with negative energy for which time flows backward. A new consequence of this interpretation is the antiphoton existence which differs from the photon by the helicity sign. Its analogues are an antigraviton and antigluons (the antiquanta of the gravitational and nuclear fields).

The monochromatics of the Moessbauer radiation is ensured by that the totality of nuclei recoiling upon itself. The estimation of the transmission speed of the corresponding interaction from a radiating nucleus to surrounding ones gives a value considerably exceeding the light velocity.

It is emphasized that the phenomena of gravitational lensing and photon frequency shift (at an atomic transition) in a gravitational field exclude each other mutually. Therefore, the results of experiments with an atomic clock (confirming the shift) call in question the truth of gravitational lensing observation.

An opinion is expressed that special relativity would be named the Lorentz-Poincare-Einstein-Minkowski relativity theory. It is noted again that these two known conclusions of general relativity contradict the results of experiments with atomic clocks and each other.

It is emphasized that black holes (BH) are not a specific consequence of general relativity. According to relativistic gravidynamics the frequency (energy) photons decreases at their emission in a gravitational field. As a result (in the limit), very massive bodies ? BH lose an ability to radiate light signals.

It is marked that the special relativity theory correlates a four-component quantity to a material rod. The corresponding limiting transition from Minkowski's 4-geometry to Euclid's 3-geometry (justified in the rest frame) is provided by vanishing the time component. It is emphasized that the interval (pseudo-length) as a Lorentzian scalar must not depend on velocity. In particular, the space-like interval is equal to the rod length at rest. In a moving frame, its space part (the rod length in motion) because of the negative sign (pseudo-Euclideanness) is always greater than the interval itself. And this means that bodies elongate (but do not contract) in motion.

The calculation of the gravitational shift of photon frequency forms the foundation for the quantum theory of gravity. The 4-vector nature of the gravitational field (its time component is Newton's potential) is its consequence. As a result, the previous difficulty of gravitational field quantization in general relativity (connected with metric quantization) is removed. That opens up the way to the construction of a united theory for all of the fundamental interactions.

Virtual field quanta carry an interaction between particles. The opinion is expressed that the difference between the fields of positive and negative charges, can be conditioned by the helical differences of the corresponding virtual photons. But some difficulties arise when one tries to explain the mechanism by which the very charge value is carried.

It can be shown that the contra-variant component of the material body energy in GR, describes a gravitational repulsion.

According to the generally accepted opinion, the electric field of a moving charge has the form of oblate revolution ellipsoid in accordance with the Lorentz contraction formula. This picture, however, contradicts the known experiment based on the gas-efflux method.

It is emphasized that the previous arguments against "antigravity" are removed within the framework of relativistic gravidynamics (the theory of gravivector field). The search for this phenomenon is of paramount importance to elucidate the nature of gravitational interaction. According to Feynman, time flows backward for antiparticles (a consequence of T-symmetry) therefore the "antigravity" absence can mean (like in the case of weak interaction) the violation of T-invariance (the "time arrow" existence).

It is shown that the velocity of light in general relativity depends not only on a gravitational potential but also on a direction. Moreover, its change across a gravitational field is half as much the generally accepted value (presenting its change along the field).

We pay attention to sensational Marmet and Couture?s paper. This paper shows how all the experiments claiming the deflection of light by the Sun are subject to very large systematic errors, which render the results highly unreliable. Theoretical analysis of this problem (based on Minkowski?s equation) is presented.

Two existing relativistic theories of gravity are compared from the viewpoint of the fulfillment of 4 of Einstein's postulates. An additional 5^th postulate of the agreement of theory with experiment is considered with the same aim.

It is shown that general-relativistic (like special-relativistic) time is larger than the proper one (gravitational time dilation). This conclusion contradicts the experiments on the gravitational time slowing down.

Additional arguments against the traditional representation of the contraction of longitudinal sizes of moving bodies are presented. It is shown that the use of noncovariant contracted length leads to violation of the laws of electric charge and energy conservation.