The correspondence to the Solar System of not the static Newtonian gravitational field, but the dynamic gravitational field, which is also formed by the motion of the planets and, therefore, adapts to changes in the location of the planets in it, is substantiated. It is because of this that gravitational pseudo-forces, like centrifugal pseudo-forces of inertia, are orthogonal at all points to the quasicircular (pseudo-elliptical) orbits of the planets.

The feasibility of using the equations of the dynamic gravitational field to reflect the expanding Universe has been proven. The fallacy of using such a false parameter as the coordinate velocity of light in GR is proven. This coordinate velocity of light, unlike the limit velocity of matter, cannot in principle be less than the true velocity of matter.

The suitability for use in the people's world of only ordinary synchronization-compensation transformations of increments of spatial coordinates and time is substantiated. These transformations, unlike the alternative to them ordinary Lorentz transformations (OLT), allow to proportionally synchronize all clocks that move in a gravitational field by inertia.

The feasibility of using the equations of the dynamic gravitational field to reflect the expanding Universe has been proven. Only thanks to this, the Hubble velocity of matter will not exceed the velocity of light at the event horizon of the Universe.

The correspondence of the parameter b of the Schwarzschild solution of the gravitational field equations to the square of the relative frequency of electromagnetic interaction of micro-objects of a stationary matter and its equivalence to the square of the maximum possible (limit) velocity of this matter on a singular surface are substantiated.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) and in its improved version – the relativistic gravithermodynamics (RGTD) is substantiated.

The feasibility of using the equations of the dynamic gravitational field to reflect the expanding Universe has been proven. Only thanks to this, the Hubble velocity of matter will not exceed the velocity of light at the event horizon of the Universe.

For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of four hidden wave functions that can take arbitrary values with certain probability.

Lorentz transformations are the transformations of only spatial coordinates and coordinate time and not of metrical spatial segments or metrical time intervals. And, therefore, it is still required to multiply the matrix of transformations of increments of coordinates by the matrix of transition to the increments of metrical segments.

The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion. For the description of the inertial motion in RGTD only the hypothetical intranuclear gravithermodynamic characteristics of matter are used.

The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion.

The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion.

The most perfect modification of the special and general theories of relativity is considered. It is shown that equations of the gravitational field of General Relativity (GR) should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR.

Neutrino is considered the carrier of gravitation. Earth gravity is formed due to the central Earth core shielding all-penetrating neutrino flow. Neutrino penetrates the Earth interfering fusion reaction on the core surface of our planet and stops motion and pressuring. As consequence neutrino is facing gravity force forwarded to the center of our planet.