  The purpose of the article is to investigate the existence of Ricci solitons
and the nature of curvature inheritance as well as collineations on the
Robinson-Trautman (briefly, RT) spacetime. It is shown that under certain
conditions RT spacetime admits almost Ricci soliton, almost $\eta$-Ricci
soliton, almost gradient $\eta$-Ricci soliton. As a generalization of curvature
inheritance \cite{Duggal1992} and curvature collineation \cite{KLD1969}, in
this paper, we introduce the notion of \textit{generalized curvature
inheritance} and examine if RT spacetime admits such a notion. It is shown that
RT spacetime also realizes the generalized curvature (resp. Ricci, Weyl
conformal, concircular, conharmonic, Weyl projective) inheritance. Finally,
several conditions are obtained, under which RT spacetime possesses curvature
(resp. Ricci, conharmonic, Weyl projective) inheritance as well as curvature
(resp. Ricci, Weyl conformal, concircular, conharmonic, Weyl projective)
collineation, and we have also introduced the concept of generalized Lie
inheritance and showed that RT spacetime realizes such a notion.
