2002/02/04 by José M. M. Senovilla, García-Parrado, Alfonso, Senovilla, José M. M. · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.math-ph/0202005
openalex publication_date 2002/02/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.