Recent Publications (links to original preprints)
- "Slicing, Threading and Parametric Manifolds", S. Boersma and
T. Dray (1995), General Relativity and Gravitation, 27,
319-339.
- We present a unified treatment of the slicing (3+1) and
threading (1+3) decompositions of spacetime in terms of foliations.
It is well-known how to decompose the metric and connection in
the slicing picture; this is at the heart of any initial-value problem in
general relativity. We describe here the analogous problem in the threading
picture, recovering the recent results of Perjes on parametric
manifolds.
- General Relativity and Quantum Cosmology Abstract 9407020
- "Parametric Manifolds. I: Extrinsic approach", S. Boersma and
T. Dray (1995), Journal of Mathematical Physics, 36,
1378-1393.
- A parametric manifold can be viewed as the manifold of
orbits of a
(regular) foliation of a manifold by means of a family of curves. If the
foliation is hypeach of
which inherits a metric and connection from the original manifold via
orthogonal projections; this is the well-known Gauss-Codazzi formalism. We
generalize this formalism to the case where the foliation is not hypersurface
orthogonal. Crucial to this generalization is the notion of deficiency,
which measures the failure of the orthogonal tangent spaces to be
surface-forming, and which behaves very much like torsion. Some applications
to initial value problems in general relativity will be briefly discussed.
- General
Relativity and Quantum Cosmology Abstract 9407011
- "Parametric Manifolds. II: Intrinsic approach", S. Boersma and
T. Dray (1995), Journal of Mathematical Physics, 36,
1394-1403.
- A parametric manifold is a manifold on which all tensor
fields depend on
an additional parameter, such as time, together with a parametric
structure, namely a given (parametric) 1-form field. Such a manifold
admits
natural generalizations of Lie differentiation, exterior differentiation, and
covariant differentiation, all based on a nonstandard action of vector fields
oures whether a parametric
manifold can be viewed as a 1-parameter family of orthogonal hypersurfaces.
- General
Relativity and Quantum Cosmology Abstract 9407012