The order on the light cone and its induced topology
Abstract
In this paper, we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his fine topology. This misconception appeared while trying to establish the causality in the ambient boundaryambient space cosmological model. We then show that this topology is actually the intersection topology (in the sense of Reed [The intersection topology w.r.t. the real line and the countable ordinals, Trans. Am. Math. Soc. 297(2) (1986) 509520]) between the Euclidean topology on &R;4 and the order topology whose order, namely horismos, is defined on the light cone and we show that the order topology from horismos belongs to the class of Zeeman topologies. These results accelerate the need for a deeper and more systematic study of the global topological properties of spacetime manifolds.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 2018
 DOI:
 10.1142/S021988781850069X
 arXiv:
 arXiv:1710.05177
 Bibcode:
 2018IJGMM..1550069P
 Keywords:

 Null cone;
 causal orders;
 horismos;
 Zeeman–Gobel topologies;
 ambient cosmology;
 topologization of a spacetime;
 Mathematical Physics
 EPrint:
 arXiv admin note: text overlap with arXiv:1706.07488