Causal Relations and their applications

Details Causal Relations and their applications Causal Relations and their applications

2002-02-04

arxiv.org/abs/math-ph/0202005v2

Physics

Mathematical Physics

Contribution to the proceedings of the 1st congress of Lorentzian Geometry held at Benalm\'{a}dena (M\'{a}laga, Spain) Replace

Scientific paper

In this work we define and study the relations between Lorentzian Manifolds given by the diffeomorphisms which map causal future directed vectors onto causal future directed vectors. This class of diffeomorphisms, called proper causal relations, contains as a subset the well-known group of conformal relations and are deeply linked to the so-called causal tensors. If two given Lorentzian manifolds are in mutual proper causal relation then they are said to be causally isomorphic: they are indistinguishable from the causal point of view. Finally, the concept of causal transformations for Lorentzian manifolds is introduced and its main mathematical properties briefly investigated.

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