Covariant approach to the conformal dynamical equivalence in astrophysics

TL;DR

This paper investigates how conformal transformations relate geodesic and hydrodynamic flows in astrophysics, revealing potential underestimations of mass when using Keplerian motion assumptions.

Contribution

It introduces a covariant framework to analyze the conformal dynamical equivalence between geodesic and hydrodynamic flows in astrophysics.

Findings

Mass density differences depend on fluid energy and pressure.

Relativistic and non-relativistic cases show distinct behaviors.

Observational mass estimates based on Keplerian motion may be underestimated.

Abstract

We use covariant techniques to examine the implications of the dynamical equivalence between geodesic motions and adiabatic hydrodynamic flows. Assuming that the metrics of a geodesically and a non-geodesically moving fluid are conformally related, we calculate and compare their mass densities. The density difference is then expressed in terms of the fundamental physical quantities of the fluid, such as its energy and isotropic pressure. Both the relativistic and the non-relativistic case are examined and their differences identified. Our analysis suggests that observational determinations of astrophysical masses based on purely Keplerian motions could underestimate the available amount of matter.