KTH/Nordita/SU seminar in Theoretical Physics [before December 2013]
Wednesday 31 October 2007
to 12:00 at
Alfonso Garcia-Parrado (MAI, Linkoping)
The notion of "causal structure" has been used in General
Relativity most of the time in connection with "conformal structure"
or "conformal equivalence". Although these concepts of causal structure
have proven themselves quite useful, there are cases in which two
spacetimes have similar causal properties but no conformal mapping
between each other exists (e. g. two weak perturbations of Minkowski
spacetime). To remedy this, the concept of "causal map" is introduced.
Causal maps generalize conformal maps and we show how
they can be used to define a new concept of causal structure which
contains the traditional one based on conformal equivalence as a
particular case. Causal structures can be sorted by means of a
partial order and we show
the extent to which this ordering generalises the classification of
spacetimes according to the "standard hierarchy of causality
conditions". We also put forward the concept of stability and
instability of the causal structure and explain how it can be applied
to examples as relevant as Minkowski or de Sitter spacetimes.
The causal structure of other well-known spacetimes (Schwarzschild,
pp-waves) is also studied with our techniques.