Geodesic motion on the group of boundary diffeomorphisms from Einstein's equations
High Energy Physics - Theory
2021-08-12 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
In arXiv:1904.12869 it was shown how in an adiabatic limit the vacuum Einstein equations on a compact spatial region can be re-expressed as geodesic equations on the group of diffeomorphisms of the boundary. This is reminiscent of the program initiated by V. Arnold to reformulate models of continuum mechanics in terms of geodesic motion on diffeomorphism groups. We revisit some of the results of arXiv:1904.12869 in this light, pointing out parallels and differences with the typical examples in geometric continuum mechanics. We work out the case of 2 spatial dimensions in some detail.
Cite
@article{arxiv.2106.13268,
title = {Geodesic motion on the group of boundary diffeomorphisms from Einstein's equations},
author = {Emine Şeyma Kutluk and Dieter Van den Bleeken},
journal= {arXiv preprint arXiv:2106.13268},
year = {2021}
}
Comments
28 pages, 2 figures. version submitted for publication