Potentials of the type $a_n/r^n$, $n>1$, in collapsing systems in general relativity

A nonlinear generalization of Maxwell's equations is constructed; it leads to static repulsive potentials of the type $a_n/r^n$, $n>1$. The corresponding analog of the Nordström– Reissner metric is constructed. It is shown that in classical, i.e., nonquantum, physics the forces, $a_n/r^{n+1}$, $n>1$, do not lead to divergences of the source selfenergy in general relativity. It is shown that if a collapsing system passes through its gravitational radius – forming a black hole – the classical forces $a_n/r^{n+1}$, $n>1$, and also the electrostatic and gravitational forces, do not vanish in the exterior space; this result contradicts Hartle's result [6] obtained for pair neutrino forces $(\sim1/r^5)$.