Estimation of almost Ricci-Yamabe solitons on static spacetimes

Abstract

This research work examines the standard static spacetime (SSST) in terms of almost Ricci-Yamabe soliton with conformal vector field. It is shown that almost Ricci-Yamabe soliton in standard static spacetime with function ? satisfies Poisson-Laplace equation. Next, we consider the function ? is harmonic and discuss the harmonic aspect of almost Ricci-Yamabe soliton on SSST. In addition, we investigate the nature of almost Ricci-Yamabe soliton on SSST with non-rotating Killing vector field. Also, we exhibit that non-steady non shrinking almost Ricci-Yamabe soliton i.e., ?? 0 on smooth, connected, and non-compact SSST with Killing vector field satisfies the Schr?dinger equation for a smooth function ?. Finally, we study almost Ricci-Yamabe soliton on static perfect fluid and vacuum static spacetime with conformal Killing vector field.