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 $\psi$ satisfies Poisson-Laplace equation. Next, we consider the function $\psi$ 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., $\lambda\geq 0$ on smooth, connected, and non-compact $SSST$ with Killing vector field satisfies the Schr\"{o}dinger equation for a smooth function $\psi$. Finally, we study almost Ricci-Yamabe soliton on static perfect fluid and vacuum static spacetime with conformal Killing vector field.