Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: dynamical equivalence and consequences

Abstract

Stimulated by the methods applied for the observational determination of masses in the central regions of the AGNs, we examine the conditions under which, in the interior of a gravitating perfect fluid source, the geodesic motions and the general relativistic hydrodynamic flows are dynamically equivalent to each other. Dynamical equivalence rests on the functional similarity between the corresponding (covariantly expressed) differential equations of motion and is obtained by conformal transformations. In this case, the spaces of the solutions of these two kinds of motion are isomorphic. In other words, given a solution to the problem hydrodynamic flow in a gravitating perfect fluid, one can always construct a solution formally equivalent to the problem geodesic motion of a fluid element and vice versa. Accordingly, we show that, the observationally determined nuclear mass of the AGNs is being overestimated with respect to the real, physical one. We evaluate the corresponding mass-excess and show that it is not always negligible with respect to the mass of the central dark object, while, under circumstances, can be even larger than the rest-mass of the circumnuclear gas involved.

Magnetohydrodynamic flows as Newtonian-type gravitational motions

“…We are motivated by the fact that almost all mass measurements made are based on the assumption of idealized purely Newtonian-type gravitational motions, although this is only approximately true at best. To find out what ignoring the actual MHD motions means for the accuracy of an obtained mass-energy estimate, we have employed a rather simple theoretical argument which extends the work of [11,12] to magnetised environments. We have shown, in particular, that the MHD flow of the actual physical fluid can be represented as a purely gravitational motion of a virtual medium under a different, generalised gravitational potential.…”

“…In the absence of a B-field the above reduces to the expression relating the density of a physical, hydrodynamically moving, Newtonian fluid to that of its virtual counterpart with a purely Newtonian motion [11,12]. In particular, the second term on the right-hand side of the above is due to the fluid pressure, while the last two primarily convey the magnetic field contribution.…”

“…Let us now focus specifically on the effects of the magnetic pressure and ignore those of the matter. In other words, assume (mainly for illustration purposes) that ∂ α 0 ∂ α ρ, referring the reader to [11,12] for a discussion on the role of nonzero pressure and density gradients. Following (32), in the pure-magnetic case we have…”

“…Here, following [11,12], we consider the magnetohydrodynamic (MHD) motion of a highly conducting, selfgravitating fluid within the framework of Newtonian theory. We first show that, under certain conditions, the MHD flow of the matter (Sec.…”

Complexity Phenomena Induced by Novel Symmetry and Symmetry-Breakings with Antiscreening at Cosmological Scales—A Tutorial

“…We end this brief tutorial by mentioning that one of the reviewers of this manuscript kindly pointed out that Kleidis and Spyrou [14] have previously suggested that dynamical equivalence between geodesic motions and hydrodynamic flows could also introduce virtue mass terms and the modification of the gravitational potential. Their idea was based on conformal transformations, whereas the CILOMAS theory is based on the scale-running of the propagator coupling constant resulting from the classical RG transformations.…”