Type and structure of timelike singularities in the general theory of relativity: from the gamma metric to the general solution

A method is proposed that makes it possible to determine whether a timelike singularity corresponds to a point, linear, or other type of gravitational field source. It is shown that in the general theory of relativity it is also possible to have sources of a quite different type with no analogs in a space of finite curvature. An analysis is made of some well-known solutions containing timelike singularities whose type varies depending on the signs of the functions that occur in the solutions. The form of the solution near simple linear sources [W. Israel, Phys. Rev. D15, 935 (1977)] and generalized anisotropic solutions [S. L. Parnovsky, Physica (Utrecht) 104A, 210 (1980); E. M. Lifshitz and I. M. Khalatnikov, Sov. Phys. Usp. 6, 359 (1963)] is determined more accurately; the space-time described by the γ metric (3) is completely investigated; and the form of the metric near the ends and singular points of linear Weyl singularities is found