Solitonic Aspect of Relativistic Magneto-Fluid Spacetime with Some Specific Vector Fields

The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci-Yamabe soliton (RY-soliton) and gradient Ricci-Yamabe soliton (GRY-soliton). We exhibit that a magneto-fluid spacetime filled with a magneto-fluid density rho, magnetic field strength H, and magnetic permeability mu obeys the Einstein field equation without the cosmic constant being a generalized quasi-Einstein spacetime manifold (GQE). In such a spacetime, we obtain an EoS with a constant scalar curvature R in terms of the magnetic field strength H and magnetic permeability mu. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci-Yamabe solitons with a time-like torse-forming vector field xi and a phi(Ric) vector field. We establish the existence of a black hole in the relativistic magneto-fluid spacetime by demonstrating that it admits a shrinking Ricci-Yamabe soliton and satisfies the time-like energy convergence criteria. In addition, we examine the magneto-fluid spacetime with a gradient Ricci-Yamabe soliton and deduce some conditions for an equation of state (EoS) omega = -1/5 with a Killing vector field. Furthermore, we demonstrate that the EoS omega = -1/5 of the magneto-fluid spacetime under some constraints represents a star model and a static, spherically symmetric perfect fluid spacetime. Finally, we prove that a gradient Ricci-Yamabe soliton with the conditions mu = 0 or H = 2; mu not equal 0, H > 2 and obeying the equation of state omega = -1/5 is conceded in a magneto-fluid spacetime, and a naked singularity with a Cauchy horizon subsequently emerges, respectively.