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Low energy limits of general relativity and galactic dynamics

Matteo Luca Ruggiero and Davide Astesiano

Vol. 11 (2023), No. 2, 271–286
DOI: 10.2140/memocs.2023.11.271
Abstract

Rotation curves of galaxies cannot be explained in terms of Newtonian gravity on the basis of the visible matter content; in fact, they become flat in the outer regions, in contrast to what is expected, and, to explain this peculiar feature, the presence of dark matter is required. In this context, Newtonian gravity rather than general relativity is used since, far from the galactic center, the gravitational field is supposed to be weak and stars are not moving at relativistic speeds. Nonetheless, there are general relativistic effects without a Newtonian counterpart, such as the gravitomagnetic effects originating from mass currents, and their impact on galactic dynamics was recently focused on. Here, we study some suitable low energy limits of an exact solution of Einstein’s equations, which can be considered as a model for the galactic dynamics, and investigate the impact of rotation effects on the density profile.

Keywords
exact solutions, galactic dynamics, general relativity
Mathematical Subject Classification
Primary: 83C15
Secondary: 83C56
Milestones
Received: 30 September 2022
Revised: 21 November 2022
Accepted: 10 January 2023
Published: 12 November 2023

Communicated by Emilio Barchiesi
Authors
Matteo Luca Ruggiero
Dipartimento di Matematica “G. Peano”
Università degli studi di Torino
Torino
Italy
Laboratorio Nazionale di Legnaro
Istituto Nazionale di Fisica Nucleare
Legnaro
Italy
Davide Astesiano
Science Institute
University of Iceland
Reykjavik
Iceland