非表示:
キーワード:
Physics, Computational Physics, physics.comp-ph,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
要旨:
Reference metrics are used to define the differential structure on multicube
representations of manifolds, i.e., they provide a simple and practical way to
define what it means globally for tensor fields and their derivatives to be
continuous. This paper introduces a general procedure for constructing
reference metrics automatically on multicube representations of manifolds with
arbitrary topologies. The method is tested here by constructing reference
metrics for compact, orientable two-dimensional manifolds with genera between
zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity
numerically to the level of truncation error (which converges toward zero as
the numerical resolution is increased). These reference metrics can be made
smoother and more uniform by evolving them with Ricci flow. This smoothing
procedure is tested on the two-dimensional reference metrics constructed here.
These smoothing evolutions (using volume-normalized Ricci flow with DeTurck
gauge fixing) are all shown to produce reference metrics with constant scalar
curvatures (at the level of numerical truncation error).
