2 research outputs found
Rigid spheres in Riemannian spaces
Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of
the Cauchy space, leads often to a substantial simplification of various
mathematical problems in General Relativity Theory. We propose a new method to
construct such foliations. For this purpose we define a special family of
topological two-spheres, which we call "rigid spheres". We prove that there is
a four-parameter family of rigid spheres in a generic Riemannian three-manifold
(in case of the flat Euclidean three-space these four parameters are: 3
coordinates of the center and the radius of the sphere). The rigid spheres can
be used as building blocks for various ("spherical", "bispherical" etc.)
foliations of the Cauchy space. This way a supertranslation ambiguity may be
avoided. Generalization to the full 4D case is discussed. Our results
generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used
by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page