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Stimulated by the methods applied for the observational determination ofmasses in the central regions of the AGNs, we examine the conditions underwhich, in the interior of a gravitating perfect fluid source, the geodesicmotions and the general relativistic hydrodynamic flows are dynamicallyequivalent to each other. Dynamical equivalence rests on the functionalsimilarity between the corresponding (covariantly expressed) differentialequations of motion and is obtained by conformal transformations. In this case,the spaces of the solutions of these two kinds of motion are isomorphic. Inother words, given a solution to the problem "hydrodynamic flow in a perfectfluid", 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 overestimatedwith respect to the real, physical one. We evaluate the correspondingmass-excess and show that it is not always negligible with respect to the massofthe central dark object, while, under circumstances, can be even larger thanthe rest-mass of the circumnuclear gas involved.Comment: LaTeX file, 22 page

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