Review
Version 1
Preserved in Portico This version is not peer-reviewed
One-Dimensional Relativistic Self-Gravitating Systems
Version 1
: Received: 9 June 2024 / Approved: 11 June 2024 / Online: 13 June 2024 (03:40:01 CEST)
A peer-reviewed article of this Preprint also exists.
Mann, R.B. One-Dimensional Relativistic Self-Gravitating Systems. Entropy 2024, 26, 612. Mann, R.B. One-Dimensional Relativistic Self-Gravitating Systems. Entropy 2024, 26, 612.
Abstract
One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature that gravitational radiation is absent, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the 2-body, 3-body, 4-body, and N-body problems. Quite general exact solutions can be obtained for the 2-body problem, unlike the situation in general relativity in 3 spatial dimensions for which only highly specified solutions exist. The 3-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For N4 other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.
Keywords
Self-Gravitating Systems; Lower-Dimensional Gravity; Relativistic Chaos
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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