Conformal vector fields for some vacuum classes of pp-waves space-times in ghost free infinite derivative gravity

Abstract

The aim of this paper is to find conformal vector fields (CVFs) for some vacuum classes of the pp-waves space-times in the ghost free infinite derivative gravity (IDG). In order to find the CVFs of the above-mentioned space-times in the IDG, first, we deduce various classes of solutions by employing a classification procedure that in turn leads towards 10 cases. By reviewing each case thoroughly by direct integration technique, we find that there exists only one case for which the space-time admits proper CVFs whereas in rest of the cases, the space-time either becomes flat or it admits homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the pp-waves space-times in the IDG has turned out to be one, two, seven or fifteen.