On the theory of homothetic and affine orbits in space time

Following recent work on the theory of Killing orbits in spacetime [1], an extension of these ideas is made to include the orbits of the homothetic and affine Lie algebras of symmetry vector fields. The possibility of a coincidence of orbits from the Killing, homothetic or affine algebras is explored and the results related to the stability of the orbits. A classification of homothetic isotropy is given and several examples of the possible orbit and isotropy behaviour are presented.