Black holes: a prediction of theory or phantasy?
We argue for black holes do not represent a strict consequence of general relativity.
gr-qc↗
arXiv subjects
A. A. Logunov
Publications and source records attributed to A. A. Logunov.
On the Boundary Behavior of Positive Solutions of Elliptic Differential Equations
Let $u$ be a positive harmonic function in the unit ball $B_1 \subset \mathbb{R}^n$ and let $μ$ be the boundary measure of $u$. Consider a point $x\in \partial B_1$ and let $n(x)$ denote the unit normal vector at $x$. Let $α$ be a number in $(-1,n-1]$ and $A \in [0,+\infty) $. We prove that $u(x+n(x)t)t^α \to A$ as $t \to +0$ if and only if $\frac{μ({B_r(x)})}{r^{n-1}} r^α \to C_αA$ as $r\to+0$, where ${C_α= \frac{π^{n/2}}{Γ(\frac{n-α+1}{2})Γ(\frac{α+1}{2})}}$. For $α=0$ it follows from the theorems by Rudin and Loomis which claim that a positive harmonic function has a limit along the normal iff the boundary measure has the derivative at the corresponding point of the boundary. For $α=n-1$ it concerns about the point mass of $μ$ at $x$ and it follows from the Beurling minimal principle. For the general case of $α\in (-1,n-1)$ we prove it with the help of the Wiener Tauberian theorem in a similar way to Rudin's approach. Unfortunately this approach works for a ball or a half-space only but not for a general kind of domain. In dimension $2$ one can use conformal mappings and generalise the statement above to sufficiently smooth domains, in dimension $n\geq 3$ we showed that this generalisation is possible for $α\in [0,n-1]$ due to harmonic measure estimates. The last method leads to an extension of the theorems by Loomis, Ramey and Ullrich on non-tangential limits of harmonic functions to positive solutions of elliptic differential equations with Holder continuous coefficients.
math.CA↗
The Effect of Accumulation of Excess Energy of a Body in Gravitational Compression
It is shown that a gravitational compression of a spherical body results in an infinite growth of the energy of a body as its radius comes close to $GM/c^2$. This gives rise to a negative defect of mass and, due to an instability, to an expansion or to an explosion. A rigorous proof of the above statement can be obtained within the General Relativity in the harmonic coordinates.
physics.gen-ph↗
Gravitational Waves in Relativistic Theory of Gravitation
It is shown that, in the framework of Relativistic Theory of Gravitation with massive graviton, gravitational waves, due to the causality condition, do not bear negative energy flows.
gr-qc↗
Repulsive force in the field theory of gravitation
It is shown that the slowing down of the rate of time referencing to the inertial time leads in the field theory of gravitation to arising of repulsive forces which remove the cosmological singularity in the evolution of a homogeneous and isotropic universe and stop the collapse of large masses.
gr-qc↗
Impossibility of Unlimited Gravitational Collapse
It is shown that the gravitational field, as a physical field developing in the Minkowsky space, does not lead to unlimited gravitational collapse of massive bodies and, hence, excludes a possibility of the formation of the ``black holes''.
gr-qc↗
On gravitational flow in the Relativistic Theory of Gravitation
A definition of the gravitational flow and a short description of the recipe of its calculation are presented.
gr-qc↗
Self-restriction of Gravitational Field and its Role in the Universe
It is shown in the article that according to the Relativistic Theory of Gravitation the gravitational field providing slowing down of the time rate nevertheless stops itself this slowing down in strong fields. So a physical tendency of this field to self-restriction of the gravitational potential is demonstrated. This property of the field leads to a stopping of the collapse of massive bodies and to the cyclic evolution of the homogeneous and isotropic Universe.
gr-qc↗
On Boundedness of the Admissible Time Slowing Down by the Gravitational Field
It is shown that there exists, in the field theory of gravitation, contrary to the General Theory of Relativity (GTR), a bound for admissible time slowing down by the gravitational field which excludes a possibility of unbounded compression of matter by the gravity forces.
gr-qc↗
On the Internal Solution of the Schwarzschild Type in the Field Theory of Gravitation
It is shown that the internal solution of the Schwarzschild type in the Relativistic Theory of Gravitation does not lead to an {infinite pressure} inside a body as it holds in the General Theory of Relativity. This happens due to the graviton rest mass, because of the stopping of the time slowing down.
gr-qc↗
The Field Theory of Gravitation and The Rest Mass of Particles
It is shown in this work that all free physical fields should have a nonzero rest mass according to the field theory of gravitation.
gr-qc↗
Henri Poincare and Relativity Theory
The book presents ideas by H. Poincare and H. Minkowski according to those the essence and the main content of the relativity theory are the following: the space and time form a unique four-dimensional continuum supplied by the pseudo-Euclidean geometry. All physical processes take place just in this four-dimensional space. Comments to works and quotations related to this subject by L. de Broglie, P.A.M. Dirac, A. Einstein, V.L. Ginzburg, S. Goldberg, P. Langevin, H.A. Lorentz, L.I. Mandel'stam, H. Minkowski, A. Pais, W. Pauli, M. Planck, A. Sommerfeld and H. Weyl are given in the book. It is also shown that the special theory of relativity has been created not by A. Einstein only but even to a greater extent by H. Poincare. The book is designed for scientific workers, post-graduates and upper-year students majoring in theoretical physics.
physics.gen-ph↗
On one fundamental property of gravitational field in the field theory
It is shown that the universal property of gravitational field to slow down the rate of time leads in the field theory to a fundamental property -- generation of effective forces of repulsion.
gr-qc↗
How Were the Hilbert--Einstein Equations Discovered?
The pathways along which A. Einstein and D. Hilbert independently came to the gravitational field equations are traced. Some of the papers that assert a point of view on the history of the derivation of the gravitational field equations ``that radically differs from the standard point of view'' are critically analyzed. It is shown that the conclusions drawn in these papers are completely groundless.
physics.hist-ph↗
Graviton Mass, Quintessence and Oscillatory Character of the Universe Evolution
It is shown that using the relativistic field theory of gravity (RTG) and measured value of $Ω_{tot}$ one can obtain the upper limit on the graviton mass with 95%C.L.: $m\leq 1.6\cdot 10^{-66}$ [g]; within the $(1σ)$ range its probable value is $m_{g}= 1.3\cdot 10^{-66}$ [g]. It is pointed out that according to RTG the presence of the quintessence is necessary to explain the Universe accelerated expansion. Experimental data on the Universe age and dark matter density allow one to determine the range of possible values of the $ν$ parameter in the equation of quintessence state and indicate characteristic time, which corresponds to the beginning and cessation of the accelerated expansion epoch, as well as the time period of the maximal expansion, which corresponds to the half-period of the oscillatory evolution of the Universe.
astro-ph↗
Graviton mass and total relative density of mass Omega_tot in Universe
It is noticed that the total relative density of mass in the Universe Omega_tot should exceed 1, i.e. Omega_tot=1+f^2/6 according to the field relativistic theory of gravity (RTG), which is free of the cosmological singularity and which provides the Euclidean character for the 3-dimensional space. Here f is the ratio of the graviton mass m_g to the contemporary value of the ``Hubble mass'' m^0_H=\hbar H_0/c^2\simeq 3,8\cdot 10^{-66}h(g) (h=0,71\pm0,07). Applying results of the experimental data processing presented in [1] an upper limit for the graviton mass is established as m_g\leq 3,2\cdot 10^{-66}g at the 95% confidence level.
astro-ph↗
The Theory Of Gravity
In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the gravitational field. The energy-momentum and the angular momentum conservation laws are fulfilled in this theory. Such an approach permits us to unambiguously construct the gravitional field theory as a gauge theory. According to the RTG, the homogeneous and isotropic Universe is to be ``flat''. It evolves cyclewise from some maximal density to the minimal one, etc. The book is designed for scientific workers, post-graduates and upper-year students majoring in theoretical physics.
gr-qc↗
The Graviton Production in a Hot Homogeneous Isotropic Universe
It is shown that the RTG predicts an opportunity of the intensive production of gravitons at the early stage of evolution of the homogeneous isotropic Universe. A hypothesis is suggested that the produced gas of gravitons could be just the ``dark matter'' which presently manifests itself as a ``missing mass'' in our Universe.
gr-qc↗