Absolute parallelism: Spherical symmetry and singularities

A one-parameter class of compatible field equations of n-frames h ^a is considered, characterized by the fact that after the substitution h ^a = HPH ^a (H = detH ^a , p is the constant depending on the dimensionality n and on the equation parameter ), the equations can be written in a trilinear form which contains the matrix H_a and its derivatives, but not H ^a . The equations remain regular for degenerated matrices H_a, if r = rank H_a ^< 2, the points with r < n being singular (if n > 1 + 1/). It is shown that there exist spherically symmetric solutions with singularities appearing for r < n; as the singularity develops, there appears a domain bounded by singular points in which, for certain values of and n, the field h ^a becomes complex.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–52, September, 1991.The author thanks I. L. Bukhbinder for his interest to this paper and useful discussions during the seminar.