INTEGRATION OF THE EINSTEIN-DIRAC EQUATIONS

The problem of exact integration of the Einstein-Dirac equation is stu died. To solve this set of equations metrics admitting complete separa tion of variables in the Dirac equation are considered. At the first s tage Stackel spaces of types (3.1) and (3.0) are studied. For the firs t case obtained solutions contain arbitrary functions depending on one variable only (five real functions for the Einstein-Weyl equations an d four real functions for the Einstein-Dirac ones). For the second one all solutions belonging to the diagonal metrics of Bianchi type 1 are found. (C) 1996 American Institute of Physics.