Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Causal Relationship: a new tool for the causal characterization of
  Lorentzian manifolds   We define and study a new kind of relation between two diffeomorphic
Lorentzian manifolds called {\em causal relation}, which is any diffeomorphism
characterized by mapping every causal vector of the first manifold onto a
causal vector of the second. We perform a thorough study of the mathematical
properties of causal relations and prove in particular that two given
Lorentzian manifolds (say $V$ and $W$) may be causally related only in one
direction (say from $V$ to $W$, but not from $W$ to $V$). This leads us to the
concept of causally equivalent (or {\em isocausal} in short) Lorentzian
manifolds as those mutually causally related. This concept is more general and
of a more basic nature than the conformal relationship, because we prove the
remarkable result that a conformal relation $\f$ is characterized by the fact
of being a causal relation of the {\em particular} kind in which both $\f$ and
$\f^{-1}$ are causal relations. For isocausal Lorentzian manifolds there are
one-to-one correspondences, which sometimes are non-trivial, between several
classes of their respective future (and past) objects. A more important feature
of isocausal Lorentzian manifolds is that they satisfy the same causality
constraints. This indicates that the causal equivalence provides a possible
characterization of the {\it basic causal structure}, in the sense of mutual
causal compatibility, for Lorentzian manifolds. Thus, we introduce a partial
order for the equivalence classes of isocausal Lorentzian manifolds providing a
classification of spacetimes in terms of their causal properties, and a
classification of all the causal structures that a given fixed manifold can
have. A full abstract inside the paper.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph