Wick rotations in 3D gravity: ML(H2)-spacetimes
(December 2004)Abstract
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so
they realize effective interactions of their ending globally hyperbolic
spacetimes of constant curvature." We develop a consistent sector of
WR-rescaling theory in 3D gravity, that, in particular, concretizes the above
guess for many geometrically finite manifolds. ML(H2)-spacetimes are solutions
of pure Lorentzian 3D gravity encoded by measured geodesic laminations of the
hyperbolic plane H2, possibly invariant by any given torsion-free discrete
isometry group G. The rescalings which correlate spacetimes of different
curvature, as well as the conformal Wick rotations towards hyperbolic
structures, are directed by the gradient of the respective canonical
cosmological times, and have universal rescaling functions that only depend on
their value. We get an insight into the WR-rescaling mechanism by studying rays
of ML(H2)-spacetimes emanating from the static case. In particular, we
determine the "derivatives" at the starting point of each ray. We point out the
tamest behaviour of the cocompact G case against the different general one,
even when G is of cofinite area, but non-compact. We analyze brocken T-symmetry
of AdS ML(H2)-spacetimes and related earthquake failure. This helps us to
figure out the main lines of development in order to achieve a complete WR
rescaling theory.
Description
citeulike