A correspondence between distances and embeddings for manifolds: New techniques for applications of the Abstract Boundary

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Whale, Ben E.¹  Scott, Susan M.¹ 

[1] Australian Natl Univ, Coll Phys & Math Sci, Ctr Gravitat Phys, Canberra, ACT 0200, Australia

关键词: General Relativity;    Abstract Boundary;    Distance;    Topological metric;    Embeddings;   

DOI  :  10.1016/j.geomphys.2010.12.013

来源: Elsevier

【 摘 要 】

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the 'edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this 'edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use. Crown Copyright (c) 2011 Published by Elsevier B.V. All rights reserved.

【 授权许可】

Free