Conformal solitons in relativistic magneto-fluid spacetimes with anti-torqued vector fields

Abstract

The kinematic and dynamic properties of relativistic spacetime in the context of relativity can be modelled by three distinct classes: shrinking, steady, and expanding. This physical framework bears a resemblance to conformal Ricci flow, where solitons serve as fixed points. Notably, within the solar system, the gravitational effects predicted by Ricci flow align with those of Einstein's gravity, ensuring consistency with all classical tests. In this article, we investigate conformal solitons, which extend the concept of Ricci solitons, within the framework of a magnetized spacetime manifold equipped with an anti-torqued vector field $\zeta$. An anti-torqued vector field is defined as one that resists rotational deformation within the fluid-spacetime structure, effectively encoding a type of constrained rotational symmetry relevant in magneto-fluid dynamics. We demonstrate that whether these conformal solitons are steady, expanding, or shrinking depends on intricate relationships among key physical parameters, including magnetic permeability, magneto-fluid density, isotropic pressure, magnetic flux, and the strength of the magnetic field.