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Local observers in stationary axisymmetric dust spacetimes

Matteo Fontana1,2,*, Sergio Luigi Cacciatori1,2,3,†, and Roberto Peron4,‡

  • *Contact author: mfontana11@uninsubria.it
  • †Contact author: sergio.cacciatori@uninsubria.it
  • ‡Contact author: roberto.peron@inaf.it
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Phys. Rev. D 114, 064076 – Published 24 September, 2026

DOI: https://doi.org/10.1103/lbht-yrb4

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.

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Phys. Rev. D 114, 064076– Published 24 September, 2026
  • Received 4 March 2026
  • Accepted 27 August 2026
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