Κεφάλαια σε Ειδικούς Τόμους

•   D1 “Hydrodynamic flows versus geodesic motions in contemporary Astrophysics and Cosmology”, N. K. Spyrou and K. Kleidis, in “New Developments in Hydrodynamics Research”, J. Ibragimov & M. A. Anisimov (eds.), Nova Science Publishers Inc. ISBN 978-1-62081-223-5, pp. 113 – 158 (2012).

In the context of both the Newtonian theory and the theory of General Relativity, we have examined the exact conditions under which, in the interior of a gravitating perfect-fluid source, the geodesic motions and the adiabatic hydrodynamic flows can be dynamically equivalent to each other. Dynamical equivalence rests on the functional similarity between the corresponding differential equations of motion. As we have found, such a similarity can be revealed by a conformal transformation between the metric tensor of the original fluid and the corresponding quantity of the (so-called) virtual fluid, in which the hydrodynamic flows are formally the same as the geodesic motions. In this case, the conformal factor involved, is, essentially, the specific enthalpy of the original fluid.

The underlying idea that led us to explore a possible equivalence between geodesic motions and hydrodynamic flows, rests in the fact that, in determining the equations of motion in the interior of an astrophysical- or/and cosmological-fluid source, all the internal physical characteristics (internal motions, pressure, etc.) of this fluid should be taken into account as sources of the gravitational field (hydrodynamic approach) and not just its mass-energy content (geodesic approach). The functional expressions determining the evolution of the various physical quantities in the original and the virtual fluid (i.e., the components of their energy–momentum tensors), are related to each other through the invariant field equations, thus guarantying that the transition from the one kind of treatment to the other is performed in a covariant way. There is a wide variety of astrophysical or/and cosmological issues, that can be treated within the context of the conformal dynamical equivalence, which extends from the solar system to the central regions of galaxies, the clusters of galaxies, and the Universe as a whole. In particular:

In the Newtonian limit, the extra (internal) contribution to the original mass-energy density results in an extra inertial-energy density and hence in an extra mass, which, by virtue of Newton’s law, gives rise to an extra force. In this framework, the celebrated Pioneer-anomaly effect, i.e., the un-expected small acceleration of the homonymous space-probe towards the Sun, may have a quite acceptable classical explanation. On larger scales, but still in the Newtonian approximation, the flat rotational curves of the disk galaxies could also be explained, on the basis of the functional similarity between the equations of the ballistic motions and the generalized Euler flows.

In the general-relativistic regime, the results associated to conformal dynamical equivalence indicate that, in the determination of the masses in the central regions of the active galactic nuclei (AGNs), the observationally determined nuclear mass is being underestimated with respect to the real physical one. On evaluating the corresponding mass deficit, we have found that, in typical cases of AGNs, it is not always negligible compared with the mass of the central dark object, and it can be comparable to the total rest mass of the circumnuclear gas involved.

Finally, on cosmological scales, and under the assumption that the dark matter (DM) can be collisional, the conformal dynamical equivalence technique could provide a reasonable and conventional explanation for several open aspects of modern Cosmology, including: (i) The extra (dark) energy needed to flatten the Universe: It can be compensated by the energy of the internal motions of a collisional-DM fluid. (ii) The observed dimming of the supernovae Ia standard candles and the apparent accelerated expansion of the Universe: Both of them can be due to the misinterpretation of several cosmologically-relevant parameters by those observers who, although living in a collisional-DM (hydrodynamic) Universe, rather, insist on adopting the collisionless-DM (geodesic) approach.

In concluding, the conformal dynamical equivalence technique appears to be a valuable tool, which enables us to take into account all the (so far) neglected degrees of freedom (hydrodynamic flows, pressure, energy of the internal motions, etc.). As we have found, these internal physical characteristics of a fluid source can reveal their influence on several parameters of astrophysical or/and cosmological significance and, therefore, serve as consistent alternative solutions to several unresolved issues of the contemporary Astrophysics and Cosmology.