Exact Fermi coordinates for a class of spacetimes

TL;DR

This paper derives exact Fermi coordinates for specific spacetimes, including anti-de Sitter, de Sitter, Schwarzschild interior solutions, and the Einstein static universe, providing insights into their geometric structure.

Contribution

It presents explicit formulas for Fermi coordinates in a broad class of spacetimes, extending previous work to include various cosmological and static solutions.

Findings

Derived exact Fermi coordinates for multiple spacetimes

Discussed maximal charts for Fermi coordinates

Enhanced understanding of spacetime geometry near observers

Abstract

We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative cosmological constant, and the Einstein static universe. Maximal charts for Fermi coordinates are discussed.