Hyperbolic conformal Ricci solitons and gradient hyperbolic conformal Ricci solitons on bulk viscous fluid string spacetime

Abstract We explore the Geometrization of hyperbolic conformal Ricci solitons and examine the properties of bulk viscous fluid string spacetime in conjunction with the hyperbolic conformal Ricci solitons in this research note. A $$\varnothing ({\mathfrak {Q}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>∅</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -vector field and a Ricci bi-conformal vector field that admits the hyperbolic conformal Ricci solitons were also used to interact with the bulk viscous fluid string spacetime. It is proven that the bulk viscous fluid string spacetime admits the hyperbolic conformal Ricci solitons with a proper $$\varnothing ({\mathfrak {Q}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>∅</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -vector field, and the bulk viscous fluid string spacetime holds Ricci collineation, then the spacetime is an Einstein manifold, and hyperbolic conformal Ricci soliton is identified as a conformal Ricci soliton. Additionally, using a scalar concircular field, we study the gradient hyperbolic conformal Ricci solitons in bulk viscous fluid string spacetime and talk about the gradient hyperbolic conformal Ricci solitons’ rate of change. Finally, using a scalar concircular field and a gradient hyperbolic conformal Ricci solitons, we calculated the energy conditions for a bulk viscous fluid string spacetime.