Solitonic Aspect of Relativistic Magneto-Fluid Spacetime with Some Specific Vector Fields
Mohd Danish Siddiqi, Fatemah Mofarreh, Sudhakar Kumar Chaubey
Abstract
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 ρ, magnetic field strength H, and magnetic permeability μ 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 μ. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci–Yamabe solitons with a time-like torse-forming vector field ξ and a φ(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) ω=−15 with a Killing vector field. Furthermore, we demonstrate that the EoS ω=−15 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 μ=0 or H=2; μ≠0, H>2 and obeying the equation of state ω=−15 is conceded in a magneto-fluid spacetime, and a naked singularity with a Cauchy horizon subsequently emerges, respectively.