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.
Canonical Wick Rotations in 3-Dimensional Gravity
BENEDETTI, RICCARDO;
2009-01-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
14/36942723962924075074055765705651886256
non disponibili
Tipologia:
Altro materiale allegato
Licenza:
Importato da Ugov Ricerca - Accesso privato/ristretto
Dimensione
76.19 kB
Formato
Adobe PDF
|
76.19 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
45/33690782224424811110113032617126545821
non disponibili
Tipologia:
Versione finale editoriale
Licenza:
Importato da Ugov Ricerca - Accesso privato/ristretto
Dimensione
1.2 MB
Formato
Adobe PDF
|
1.2 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Benedetti_Preprint.PDF
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
1.63 MB
Formato
Adobe PDF
|
1.63 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.