Scalar solitons in a 4-dimensional curved space-time

There is a theorem known as a Virial theorem that restricts the possible ex istence of non-trivial static solitary waves with scalar fields in a flat s pace-time with 3 or more spatial dimensions. This raises the following ques tion: Does the analogous curved space-time version hold? We investigate the possibility of solitons in a 4-D curved space-time with a simple model usi ng numerical analysis. We found that there exists a static solution of the proposed non linear wave equation. This proves that in curved space-time th e possibilities of solitonic solutions is enhanced relative to the flat spa ce-time case.