Consequences of nonlinearity in the generalized theory of gravitation

This paper contains, for the time-independent spherically symmetric fields, various regular solutions of the field equations. The spectrum of magnetic charges ${\mathcal{I}}_n$, $n=0, 1, 2, \dots$, with alternating signs has been obtained as a function of mass where ${\mathcal{I}}_n\to 0$ for $n\to \infty$ and where ${\Sigma }_{n=0\mathrm{}}^{\infty }{\mathcal{I}}_n=0\mathrm{}$. The neutral magnetic core of an elementary particle consists of an infinite number of stratified layers containing magnetic charges of amounts ${\mathcal{I}}_n$. The screening caused by the stratified distribution of magnetic charges generates short-range forces. The strength of the coupling between the field and particle is described by $e^2+{{\mathcal{I}}_n}^2$, where $n=\infty$ corresponds to the distances beyond which there are no short-range forces. The observed mass $M$ of a particle or antiparticle is obtained, as a consequence of the equations of motion, in the form $M{c}^2=\frac{1}{2}m{c}^2+2\mathrm{}{E}_s$, where $E_s$ is the finite self-energy of the particle (or antiparticle) and where $m$ and $E_s$ have opposite signs. The "bare gravitational mass" $m$, obtained as a constant of integration, is estimated to be of the order of ${10}^{21}$ MeV. The spectrum of fundamental lengths $r_{0n}(=[\frac{{\left(2\mathrm{}{G}_0\right)}^{\frac{1}{2}}}{c^2}\left]{(e^2+{{\mathcal{I}}_n}^2)}^{\frac{1}{2}}\sim {10}^{-33\mathrm{}} \mathrm{cm}\right)$ measures the deviation of the theory from general relativity. The self-energy $E_s$ in the limit $r_{0n}=0\mathrm{}$ tends to infinity and the solutions reduce to the corresponding spherically symmetric solutions in general relativity. The spin ½ of an elementary particle is found to be the result of the assumption ${{\mathcal{I}}_n}^2={\gamma }_n\hslash c$ with ${\lim }_{n\to \infty }{\gamma }_n=0\mathrm{}$ and its neutral magnetic structure, where the latter exists only for nonvanishing ${\Gamma }_{\left[\mu \nu \right]}^{\rho }$, the antisymmetric part of the affine connection. The two states of spin correlate with the two possible sequences of signs of ${\mathcal{I}}_n$, i.e., ${\mathcal{I}}_n$ and $-{\mathcal{I}}_n$, $n=0, 1, 2, \dots$. For the solutions where $e=0\mathrm{}$ the symmetries of charge conjugation and parity are not conserved. The latter lead to the assumption of small masses for the two neutrinos ${\nu }_e$, ${\nu }_{\mu }$. Conservation of the electric charge multiplicity, i.e., the existence of -1, +1, 0 units of electric charge, is found to be the basis for the existence of four massive fundamental particles $p$, $e$, ${\nu }_e$, ${\nu }_{\mu }$ and the corresponding antiparticles $\overline{p}$, $e^{+}$, ${\overline{\nu }}_e$, ${\overline{\nu }}_{\mu }$. Based on a new concept of "vacuum" and new magnetic charge predicted by the theory it may be possible to construct all other elementary particles as bound or resonance states of the "fundamental quartet" $p$, $e$, ${\nu }_e$, ${\nu }_{\mu }$ and the "antiquartet" $\overline{p}$, $e^{+}$, ${\overline{\nu }}_e$, ${\overline{\nu }}_{\mu }$.