Related papers: A note on causally simple and globally hyperbolic …
The classical definition of {\em global hyperbolicity} for a spacetime $(M,g)$ comprises two conditions: (A) compactness of the diamonds $J^+(p)\cap J^-(q)$, and (B) strong causality. Here we show that condition (B) can be replaced just by…
This paper has been withdrawn by the author, because it is now part of an enlarged version entitled "Time functions as utilities" arXiv:0909.0890
Paper withdrawn due to conceptual mistakes. A corrected version will soon be available at the gr-qc archive.
This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.
This paper has been withdrawn by the authors. Significantly revised versions of the results of this paper are now available in arXiv:0707.0487v2 and arXiv:0808.3169v1.
This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0507018), in a clearer way.
This paper has been withdrawn by the authors due to the inconsistency of the computations used for extra dimensions and the fractal dimensional approach of the paper. An updated version of the paper will be published under a different…
This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.
Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…
Reasonable spacetimes are non-compact and of dimension larger than two. We show that these spacetimes are globally hyperbolic if and only if the causal diamonds are compact. That is, there is no need to impose the causality condition, as it…
This paper was withdrawn by the authors because it has been supplanted by gr-qc/0311007 and gr-qc/0311038.
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
This paper has been withdrawn. A much-improved version can be found at hep-ph/0209176.
We prove that there are globally hyperbolic spacetimes $(X,g)$ which are refocusing but not strongly refocusing. In fact, every globally hyperbolic strongly refocusing spacetime of dimension at least $3$ admits globally hyperbolic metrics…
This paper has been withdrawn by the author due to it contains some errors. A corrected treatment is presented in further publications of the author.
This paper has been withdrawn by the author.
This paper has been withdrawn by the author due to inconsistency of the considered working hypothesis. The consistent treatment is presented in the last publications of the author.
They are possible other cases at first done not contemplate. This paper has been withdrawn by the author due to a crucial sign error in equation 1 page 4
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
This paper has been withdrawn by the author, since some results of the paper have been already obtained in [J.~Lewandowski, Class. Quantum Grav. 9 (1992), no. 10, L147--L151.]