Imperfect Fluid Generalized Robertson Walker Spacetime Admitting Ricci-Yamabe Metric
Ali H. Alkhaldi, Mohd Danish Siddiqi, Meraj Ali Khan, Lamia Saeed Alqahtani
Abstract
In the present paper, we investigate the nature of Ricci-Yamabe soliton on an imperfect fluid generalized Robertson-Walker spacetime with a torse-forming vector field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>ξ</a:mi></a:math> . Furthermore, if the potential vector field <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>ξ</c:mi></c:math> of the Ricci-Yamabe soliton is of the gradient type, the Laplace-Poisson equation is derived. Also, we explore the harmonic aspects of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"><e:mi>η</e:mi></e:math> -Ricci-Yamabe soliton on an imperfect fluid <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"><g:mtext>GRW</g:mtext></g:math> spacetime with a harmonic potential function <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M5"><i:mi>ψ</i:mi></i:math> . Finally, we examine necessary and sufficient conditions for a <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M6"><k:mn>1</k:mn></k:math> -form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M7"><m:mi>η</m:mi></m:math> , which is the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M8"><o:mi>g</o:mi></o:math> -dual of the vector field <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M9"><q:mi>ξ</q:mi></q:math> on imperfect fluid <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" id="M10"><s:mtext>GRW</s:mtext></s:math> spacetime to be a solution of the Schrödinger-Ricci equation.