7 research outputs found
Gurses' Type (b) Transformations are Neighborhood-Isometries
Following an idea close to one given by C. G. Torre (private communication),
we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses
type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or,
equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and
I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric,
i.e., every point x in M has a corresponding diffeomorphism phi of a
neighborhood V of x onto a generally different neighborhood W of x such that
phi*(h|W) = g|V.Comment: 10 pages, LATEX, FJE-93-00
Generalized Symmetries of the Einstein Equations
We reformulate the symmetries of Gurses [Phys. Rev. Lett. 70, 367 (1993)] in
a more abstract, more geometrical manner. The type (b) transformation of
\gurses\ is related to a diffeomorphism of the differentiable manifold onto
itself. The type (c) symmetry is replaced by a more general type (c-bar)
symmetry that has the nice property that the commutator of a type (c-bar)
generator with a type (a) generator is itself of type (c-bar). We identify a
differential constraint that transformations of type (c) and (c-bar) must
satisfy, and which, in our opinion, may severely limit the usefulness of these
transformations.Comment: 22 pages, LaTeX document, report FJE-93-00