Canonical Wick rotations in 3-dimensional gravity
| dc.creator | Benedetti, Riccardo | |
| dc.creator | Bonsante, Francesco | |
| dc.date | 2005-08-25 | |
| dc.date | 2006-10-25 | |
| dc.date.accessioned | 2026-07-07T06:42:50Z | |
| dc.date.available | 2026-07-07T06:42:50Z | |
| dc.description | We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete Cauchy surface (in particular a compact one), as well as complex projective structures on arbitrary surfaces, are all encoded by pairs (H,L), H being a ``straight convex sets'' in the hyperbolic plane, and L a ``measured geodesic laminations'' suitably defined on H. (b) Canonical geometric correlations: spacetimes of different curvature, that share a same encoding pair (H,L), are related to each other by ``canonical rescaling''; they can be transformed by ``canonical Wick rotations'' in hyperbolic 3-manifolds, that carry asymptotically the corresponding projective structures. Both Wick rotations and rescalings act along the "canonical cosmological time" and have ``universal rescaling functions''. These correlations are functorial with respect to isomorphisms of the respective geometric categories. We analyze the behaviour along a ray of measured laminations, (broken) T-symmetry by spacetimes of negative curvature, the relationship with ``earthquake theory'', beyond the case of compact Cauchy surface. WR-rescaling does apply on the ``ends'' of geometrically finite hyperbolic 3-manifolds, that hence realize concrete interactions of their globally hyperbolic ``ending spacetimes'' of constant curvature. It also provides further "classical amplitudes" of these interactions, beyond the volume of the hyperbolic convex cores. | |
| dc.description | Monograph, 201 pages, 18 figures. This is a substantially reorganized version which incorporates the contents of earlier authors preprint arXiv:math.DG/0412470. To appear in Memoirs of AMS | |
| dc.identifier | https://arxiv.org/abs/math/0508485 | |
| dc.identifier | http://arxiv.org/abs/math/0508485 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102193 | |
| dc.subject | Differential Geometry | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C25; 57M50 | |
| dc.title | Canonical Wick rotations in 3-dimensional gravity | |
| dc.type | text |