Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 9

Geodesic motion on the group of boundary diffeomorphisms from Einstein’s equations

Pages: 3159 – 3187

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n9.a8

Authors

Emine Şeyma Kutluk (Middle East Technical University, Ankara, Turkey)

Dieter van den Bleeken (Department of Physics, Boğaziçi University, Istanbul, Turkey; and Institute for Theoretical Physics, KU Leuven, Belgium)

Abstract

In $\href{https://doi.org/10.1007/JHEP01(2020)184}{[16]}$ 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 $\href{https://doi.org/10.1007/JHEP01(2020)184}{[16]}$ 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.

Published 30 October 2023