doiSerbia

Proper semiconformal symmetries of spacetimes with divergence-free semiconformal curvature tensor

Ali Musavvir (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India)
Pundeer Naeem Ahmad (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India)
Suh Young Jin (Department of Mathematics and RIRCM, Kyungpook National University, Taegu, South Korea)

In the present paper, the symmetries admitted by semiconformal curvature tensor in semiconformally symmetric spacetime have been studied and we show that a four-dimensional spacetime admitting a proper semiconformal symmetry is semiconformally flat or of the Petrov type N. It is also shown that a four-dimensional spacetime with divergence-free semiconformal curvature tensor admitting a proper semiconformal symmetry is locally of the Petrov type O or has four distinct principal null directions. In both the cases, we found that if the spacetime admits an infinitesimal semiconformal Killing vector field then the scalar curvature of the spacetime vanishes.

Keywords: curvature tensors, gravitational fields, collineations