Physical frames along circular orbits in stationary axisymmetric spacetimes

TL;DR

This paper investigates the relationships between three natural orthonormal frame classes along circular orbits in stationary axisymmetric spacetimes, with applications to black hole spacetimes, enhancing understanding of local frame properties in these geometries.

Contribution

It analyzes and compares Frenet-Serret, Fermi-Walker, and parallel transported frames along circular orbits in stationary axisymmetric spacetimes, including black hole solutions, providing new insights into their interrelations.

Findings

Relationships between frame types are characterized.

Applications to black hole spacetimes are demonstrated.

Enhanced understanding of local frame behavior in stationary axisymmetric spacetimes.

Abstract

Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi-Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in stationary axisymmetric spacetimes, and illustrated for black hole spacetimes.