Dhriti Sundar Patra
Contact GRA solitons and applications to general relativity
We thoroughly examine generalized Ricci almost solitons (GRA solitons), including the gradient case on contact metric manifolds. First, we prove that a complete K-contact or Sasakian manifold with a closed GRA soliton satisfying $4c_1c_2 \neq 1$ is compact Einstein with scalar curvature $2n(2n+1)$, and for the gradient case, it is isometric to the unit sphere $\mathbb{S}^{2n+1}$. Next, we find sufficient conditions under which a non-trivial complete K-contact manifold with a GRA soliton is trivial (Einstein or $\eta$-Einstein) under the assumption that the potential vector field is conformal. Next, we prove some results on the $H$-contact and complete contact manifolds. We provide a few applications of GRA solitons in general relativity, where we find sufficient conditions for a GRW spacetime to be a PF spacetime and then characterize PF spacetimes having a concircular velocity vector field.
