Fermi-normal coordinates for the Newtonian approximation of gravity

Autor:	Gutiérrez-Piñeres, Antonio C.
Rok vydání:	2022
Předmět:	General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	In this work, we compute the metric corresponding to a static mass distribution in the general relativistic weak field approximation to quadratic order in Fermi-normal coordinates surrounding a radial geodesic. To construct a geodesic and a convenient tetrad transported along it, we first introduce a general metric, use the Cartan formalism of differential forms, and then specialize the space-time by considering the nearly Newtonian metric. This procedure simplifies the calculations significantly, and the expression for the radial geodesic admits a simple form. We conclude that in quadratic order, the effects of a Schwarzschild gravitational field measured locally by a freely falling observer equals the measured by an observer in similar conditions in the presence of a Newtonian approximation of gravitation. Comment: Added references and corrected some typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.12780 Zobrazit plný text záznamu View this record from Arxiv