Local observers in stationary axisymmetric dust spacetimes

Abstract

In this work, we construct a locally inertial reference system adapted to a geodesic observer in stationary, axisymmetric dust solutions of the Einstein equations employed as effective models of a portion of a galactic disc. To ensure a consistent spatial orientation among different local observers, we also introduce the radially locked reference system, in which one spatial axis is aligned with the radial direction defined by null geodesics passing through the galactic center. Within this framework, we analyze how the dust configuration is described by such observers by computing the frequency shift of photons exchanged between pairs of dust geodesics. Building on this construction, we outline a procedure to reconstruct spectroscopic and astrometric relative velocities with respect to locally inertial observers, providing a coherent foundation for the study of galactic kinematics in a fully general relativistic context.

Figures (6)

• Figure 2.1: $\eta(r,0)$ as a function of $r$. The parameters values are: $v_{0} = 200km\per s \simeq 7\times 10^{-4}$, $r_{0} = 1k\parsec$, $R = 100k\parsec$, as in BG.
• Figure 2.2: $\mu(r,0)$ as a function of $r$. The parameters values are: $v_{0} = 200km\per s \simeq 7\times 10^{-4}$, $r_{0} = 1k\parsec$, $R = 100k\parsec$, as in BG.
• Figure 2.3: Left panel: $\rho(r,0)$ as a function of $r$. Right panel: zoomed view near the origin. The parameters values are: $v_{0} = 200km\per s \simeq 7\times 10^{-4}$, $r_{0} = 1k\parsec$, $R = 100k\parsec$, as in BG.
• Figure 3.1: Schematic illustration of the definition of the kinematic relative velocity (adapted from 2007CMaPh.273..217B).
• Figure 3.2: Schematic illustration of the definition of the spectroscopic relative velocity (adapted from 2007CMaPh.273..217B).