Title |
Spacelike Singularities and Hidden Symmetries of Gravity
|
---|---|
Published in |
Living Reviews in Relativity, April 2008
|
DOI | 10.12942/lrr-2008-1 |
Pubmed ID | |
Authors |
Marc Henneaux, Daniel Persson, Philippe Spindel |
Abstract |
We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity. |
Mendeley readers
Geographical breakdown
Country | Count | As % |
---|---|---|
India | 2 | 6% |
United Kingdom | 1 | 3% |
Spain | 1 | 3% |
China | 1 | 3% |
Unknown | 31 | 86% |
Demographic breakdown
Readers by professional status | Count | As % |
---|---|---|
Student > Ph. D. Student | 11 | 31% |
Researcher | 7 | 19% |
Professor | 5 | 14% |
Student > Master | 4 | 11% |
Other | 2 | 6% |
Other | 4 | 11% |
Unknown | 3 | 8% |
Readers by discipline | Count | As % |
---|---|---|
Physics and Astronomy | 24 | 67% |
Mathematics | 4 | 11% |
Engineering | 2 | 6% |
Psychology | 1 | 3% |
Unknown | 5 | 14% |