Event horizon of the Tomimatsu-Sato metrics

Abstract

Recen t ly GIBBOI~'S and RUSSEL-CLAltK (1) have s ta ted t h a t our new solution (3) to E ins t e in ' s v a c u u m field equat ion does n o t conta in an even t horizon. Af te r the publ ica t ion of this new solution, which is a s ta t ionary , ax i symmet r ic , a sympto t i ca l ly flat, exac t solution, we have fu r ther found an in te res t ing series of exac t solutions (a) including the Ker r solution and the above new solut ion as special members . This new series of solutions, which we call the T-S solutions hereaf ter , e~)ntain the three parameters , i.e. the mass m, t he angular m o m e n t u m J ( ~ m2q) and the dis tor t ion pa rame te r 6, which specifics t he W e y l solutions in the s ta t ic case of q = 0. Fo r example, the quadrupole momen t s of the g rav i t a t iona l fields are given as