arXiv subjects
Publications and source records attributed to Dmitriy Palatnik.
In this letter I suggest possible redefinition of mass density, not depending on speed of the mass element, which leads to a more simple stress-energy for an object. I calculate energy of black hole.
Suggested non-linear, non-gauge modification of the Maxwell theory of electromagnetism based on correlation between electromagnetic potential, $A_a$, and metric, $g_{ab}$, such that tensor $G_{ab} = g_{ab} - l^2{A}_a{A}_b$ represents observable metric. Here $l$ is fundamental constant of the theory. The idea, that the charge density of elementary particle could be a function of electromagnetic potential and background metric (only) is accepted, and specific model of the density is considered. Due to non-linearity of equations, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} = -{(2n+1)\over3}e$, where $n = 0, 1, 2, ...$
From non-linear modification of Maxwell-Einstein theory, considered in (physics/9801031), follows modified Coulomb law for interaction between charged objects. Namely, if $(m, e)$ and $(m', e')$ are masses and charges of two objects, then the potential energy of interaction, $V(r) = [ee' - kmm' - \sqrt{k}(em' + e'm)]/r $, where $k$ is Newtonian constant. It follows, that the Earth should possess negative electric charge, $Q_E = - \sqrt{k} M_E$. Obtained result explains, why do primary cosmic rays consist mainly of positive charges.
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schrödinger equation. For mass and charge densities of electron the expressions from (physics/9811048) are taken. The energy quantizing demands quantizing of parameters $ν$ and $q$, as well as $m$ and $e$.
Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\tilde{g}}_{ab} = g_{ab} - l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations), $A_a$ is electromagnetic potential, and $l$ is fundamental constant of the theory. Specific model of the mass and charge densities of a fundamental particle is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} = -{(2n+1)\over3}e$, where $n = 0, 1, 2, ...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' - \sqrt k(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E = - \sqrt k M_E$, which explains why primary cosmic rays consist mainly of positively charged particles. One may attribute the fairweather electric field at the Earth's surface to the charge $Q_E$.
This note suggests a generalization of the Born--Infeld action (1932) on case of electroweak and gravitational fields in four-dimensional spacetime. The action is constructed from Dirac matrices, $γ_a$, and dimensionless covariant derivatives, $π_{a} = - i\ell \nabla_{a}$, where $\ell$ is of order of magnitude of Planck's length. By a postulate, the action possesses additional symmetry with respect to global transformations of the Lorentz group imposed on pairs ($γ_{a}$, $π_{a}$). It's shown, that parameter of the Lorentz group is associated with a constant value of the electroweak potential at spatial infinity. It follows, that in linear and quadratic in $\ell^2$ approximation, action for gravitational field coincides with Einstein-Hilbert (EH) and Gauss-Bonnet (GB).
This paper has been withdrawn due to submission of subsequent versions as a new preprint
This paper has been withdrawn due to upload of another version of it as a new preprint: gr-qc/0404097
This paper suggests a generalization of the Born--Infeld action (1932) for the case of electroweak and gravitational fields. Basic notions one deals with are Dirac matrices, $γ_{a}$, and dimensionless covariant derivatives, $π_{a} = - i\ell \nabla_{a}$, given in spinorial and scalar representations. The action contains a characteristic length $\ell$ (which is of order of magnitude of Planck's length), as a parameter and possesses an extra symmetry with respect to transformations of the Lorentz group imposed on pairs ($γ_{a}$, $π_{a}$). It's shown that parameter of the Lorentz group is associated with a constant value of the electroweak potential at spatial infinity.
Preprint is withdrawn, since result isn't new.
In this note one suggests a possibility of direct observation of the $θ$-parameter, introduced in the Born--Infeld theory of electroweak and gravitational fields, developed in quant-ph/0202024. Namely, one may treat $θ$ as a universal constant, responsible for correction to the Coulomb and Newton laws, allowing direct interaction between electrical charges and masses.
In this paper attention is focused on gravitational sector of the Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for gravitational field are derived. The asymptotic for modified Schwarzschild solution is obtained, as a decomposition in parameter $L \approx 10^{-32}$ cm. It is shown, that singularity at $r = 0$ is absent, being replaced by a `ball of matter' with finite dimensions, such that density of matter is of order of magnitude of the Planck's density. Another solution of the same symmetry is obtained, corresponding to a closed space of finite volume of order $L^3$.