Gurses' Type (b) Transformations are Neighborhood-Isometries

Details Gurses' Type (b) Transformations are Neighborhood-Isometries Gurses' Type (b) Transformations are Neighborhood-Isometries

1993-04-09

arxiv.org/abs/gr-qc/9304013v1

Phys.Rev.Lett. 71 (1993) 316-319

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, LATEX, FJE-93-003

Scientific paper

10.1103/PhysRevLett.71.316

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.

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