Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes

TL;DR

This paper constructs explicit Fermi coordinates in de Sitter and G"odel spacetimes, analyzes test particle dynamics, compares with Jacobi equations, and discusses challenges in black-hole spacetimes.

Contribution

It provides explicit constructions of Fermi coordinates in specific spacetimes and examines their applicability and limitations for tidal dynamics analysis.

Findings

Explicit Fermi coordinates are constructed for de Sitter and G"odel spacetimes.

Comparison shows the validity range of generalized Jacobi equations.

Demonstrates difficulties in constructing Fermi coordinates in black-hole spacetimes.

Abstract

Fermi coordinates are directly constructed in de Sitter and Goedel spacetimes and the corresponding exact coordinate transformations are given explicitly. The quasi-inertial Fermi coordinates are then employed to discuss the dynamics of a free test particle in these spacetimes and the results are compared to the corresponding generalized Jacobi equations that contain only the lowest-order tidal terms. The domain of validity of the generalized Jacobi equation is thus examined in these cases. Furthermore, the difficulty of constructing explicit Fermi coordinates in black-hole spacetimes is demonstrated.