Fermi coordinates and static observer in Schwarzschild spacetime

TL;DR

This paper presents a straightforward analytical method to construct Fermi coordinates along any line in spacetime, extending Eddington's approach, and demonstrates its application for a static observer in Schwarzschild spacetime.

Contribution

It introduces a new simple analytical approach to Fermi coordinate construction that avoids orthogonal frames and parallel transport, applied to Schwarzschild spacetime.

Findings

Successfully derived Fermi coordinates for a static observer in Schwarzschild spacetime.

Extended Eddington's approach to a more general and practical construction of Fermi coordinates.

Provided a method that simplifies the calculation of Fermi coordinates in curved spacetime.

Abstract

In this paper we construct the Fermi coordinates along any arbitrary line in simple analytical way without use the orthogonal frames and their parallel transport. In this manner we extend the Eddington approach to the construction of the Fermi metric in terms of the Riemann tensor. In the second part of the present article we show how the proposed approach works practically by applying it for deriving the Fermi coordinates for the static observer in the Schwarzschild spacetime.