D O C . 9 1 R E L AT I V I T Y & E Q U AT I O N S O F M O T I O N 9 9 . (12) The are supposed to be independent of the spacelike coordinates, but they can depend upon the time in an arbitrary way. This approach satisfies equation (7). It can differ from the representation of the actual gravitational field[24] present only by terms that correspond to the inhomogeneity of the external gravita- tional field. We shall not go into the investigation of the influence of such inhomo- geneities on the motion of the singularity. We assume that the internal gravitational field is centrally symmetric, which is certainly permissible in the first approximation. Equations (7) are known1 to be ful- filled by the following trial functions for the :[25] . (13) The sum of the trial functions (12) and (13) represents the of the overall grav- itational field in the neighborhood of the singular point, i.e., for small , to a sufficient precision. The electric field can be represented in first approximation in agreement with (10) in the neighborhood of the singularity by the trial function . (14) [26] 1 The units for m and  are chosen in such a way that the gravitational constant and the coefficient of the current density in Maxwell’s equations are set equal to 1. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a l x l        a l l 1 2 3   =  g  m 4 --------- - – 0 0 0 0 m 4 --------- - – 0 0 0 0 m 4 --------- - – 0 0 0 0 + m 4 ----------              g  x 1 , x 2 , x 3 [p. 240]  23  31  12  14  24  34 h x h y h z –ie x –ie y –ie z 0 0 0 x 1 4 3 –i------------ x 2 4 3 –i------------ x 3 4 3 –i------------          i –1 = 