Cosmological Singularities, Billiards and Lorentzian Kac-Moody Algebras
| dc.creator | Damour, Thibault | |
| dc.date | 2004-12-21 | |
| dc.date.accessioned | 2026-07-07T03:29:17Z | |
| dc.date.available | 2026-07-07T03:29:17Z | |
| dc.description | The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimension D and for the particular Einstein-matter systems arising in String theory, the billiard tables describing asymptotic cosmological behaviour are found to be identical to the Weyl chambers of some Lorentzian Kac-Moody algebras. In the case of the bosonic sector of supergravity in 11 dimensional spacetime the underlying Lorentzian algebra is that of the hyperbolic Kac-Moody group E_{10}, and there exists some evidence of a correspondence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E_{10} / K (E_{10}), where K (E_{10}) is the maximal compact subgroup of E_{10}. | |
| dc.description | 23 pages, 3 figures, contribution to the Deserfest proceedings | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0412105 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0412105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/35159 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Astrophysics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Cosmological Singularities, Billiards and Lorentzian Kac-Moody Algebras | |
| dc.type | text |