High Symmetry Fields and the Homogeneous Field in General Relativity

The usual definition of a homogeneous field in general relativity implies a space with R_iklm = 0, thus admitting a group of motions isomorphic to the Poincaré group. After discussing the symmetry group of the homogeneous field in Newtonian space, we point out that there exists no space with R_ik = 0, which is a ``true'' field, i.e., R_iklm ≠ 0, and which admits an analogous relativistic group. We then study fields, solutions of R_ik = 0, which define spaces that admit a 4‐parameter group of motions locally isomorphic to the groups $T_1{\mathrm{\otimes \; [T}}_2{\otimes }_s\text{O(2)]}$ and $T_1{\mathrm{\otimes \; [T}}_2{\otimes }_s\text{O(1,1)].}$ We compare the motion of a test particle in these fields with the motion in the usual homogeneous field.