We introduced and discussed the idea of hyperbolic Ricci-Yamabe solitons associated with perfect fluid spacetime in this research note. Additionally, we examine a perfect fluid spacetime, which accommodates the hyperbolic Ricci-Yamabe solitons and the rate of change of the hyperbolic Ricci-Yamabe solitons coupled with a conformal vector field, \(\varphi (\mathcal {Q})\) -vector field with Ricci collineation condition. We also analyze the rate of change of the hyperbolic Ricci soliton and investigate the gradient hyperbolic Ricci-Yamabe soliton on perfect fluid spacetime with scalar concircular field. Furthermore, we investigate the energy conditions for perfect fluid spacetime in terms of gradient hyperbolic Ricci-Yamabe solitons with a scalar concircular field. In the end, we introduced a more generic notion of \(\eta \) -hyperbolic Ricci-Yamabe solitons and proved that a spacetime admitting the \(\eta \) -hyperbolic Ricci-Yamabe solitons with a conformal vector field is a perfect fluid spacetime.

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Hyperbolic Ricci-Yamabe Solitons and \(\eta \) -Hyperbolic Ricci-Yamabe Solitons

  • Mohd Danish Siddiqi

摘要

We introduced and discussed the idea of hyperbolic Ricci-Yamabe solitons associated with perfect fluid spacetime in this research note. Additionally, we examine a perfect fluid spacetime, which accommodates the hyperbolic Ricci-Yamabe solitons and the rate of change of the hyperbolic Ricci-Yamabe solitons coupled with a conformal vector field, \(\varphi (\mathcal {Q})\) -vector field with Ricci collineation condition. We also analyze the rate of change of the hyperbolic Ricci soliton and investigate the gradient hyperbolic Ricci-Yamabe soliton on perfect fluid spacetime with scalar concircular field. Furthermore, we investigate the energy conditions for perfect fluid spacetime in terms of gradient hyperbolic Ricci-Yamabe solitons with a scalar concircular field. In the end, we introduced a more generic notion of \(\eta \) -hyperbolic Ricci-Yamabe solitons and proved that a spacetime admitting the \(\eta \) -hyperbolic Ricci-Yamabe solitons with a conformal vector field is a perfect fluid spacetime.