Geodesic
Potentials of the type $a_n/r^n$, $n>1$, in collapsing systems in general relativity
Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 2, pp. 153-163 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $(\sim1/r^5)$. 
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     author = {V. A. Berezin and M. A. Markov},
     title = {Potentials of the type $a_n/r^n$, $n>1$, in collapsing systems in general relativity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {153--163},
     year = {1972},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_12_2_a0/}
}
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V. A. Berezin; M. A. Markov. Potentials of the type $a_n/r^n$, $n>1$, in collapsing systems in general relativity. Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 2, pp. 153-163. http://geodesic.mathdoc.fr/item/TMF_1972_12_2_a0/

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