356 research outputs found
Computability of the causal boundary by using isocausality
Recently, a new viewpoint on the classical c-boundary in Mathematical
Relativity has been developed, the relations of this boundary with the
conformal one and other classical boundaries have been analyzed, and its
computation in some classes of spacetimes, as the standard stationary ones, has
been carried out.
In the present paper, we consider the notion of isocausality given by
Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out
isocausal comparisons with standard stationary spacetimes. As a consequence,
the qualitative behavior of the c-boundary (at the three levels: point set,
chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the
inclusion of Figure
Isocausal spacetimes may have different causal boundaries
We construct an example which shows that two isocausal spacetimes, in the
sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which
are not equal (more precisely, not equivalent, as no bijection between the
completions can preserve all the binary relations induced by causality). This
example also suggests that isocausality can be useful for the understanding and
computation of the c-boundary.Comment: Minor modifications, including the title, which matches now with the
published version. 12 pages, 3 figure
Spinor calculus on 5-dimensional spacetimes
Penrose's spinor calculus of 4-dimensional Lorentzian geometry is extended to
the case of 5-dimensional Lorentzian geometry. Such fruitful ideas in Penrose's
spinor calculus as the spin covariant derivative, the curvature spinors or the
definition of the spin coefficients on a spin frame can be carried over to the
spinor calculus in 5-dimensional Lorentzian geometry. The algebraic and
differential properties of the curvature spinors are studied in detail and as
an application we extend the well-known 4-dimensional Newman-Penrose formalism
to a 5-dimensional spacetime.Comment: Convention mismatch and minor typos fixed. To appear in Journal of
Mathematical Physic
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