The order on the light cone and its induced topology

@article{Papadopoulos2017TheOO,
  title={The order on the light cone and its induced topology},
  author={Kyriakos Papadopoulos and Santanu Acharjee and Basil K. Papadopoulos},
  journal={International Journal of Geometric Methods in Modern Physics},
  year={2017},
  volume={15},
  pages={1850069}
}
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 boundary-ambient 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) 509–520]) between… 
View PDF on arXiv
7 Citations
Background Citations
3

7 Citations

Citation Type

Citation Type

On two topologies that were suggested by Zeeman
The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such…
Space-time Singularities vs. Topologies in the Zeeman—Göbel Class
We first observe that the Path topology of Hawking, King and MacCarthy is an analogue, in curved space-times, of a topology that was suggested by Zeeman as an alternative topology to his so-called…
Natural vs. Artificial Topologies on a Relativistic Spacetime
Consider a set M equipped with a structure ∗. We call a natural topology T∗, on (M, ∗), the topology induced by ∗. For example, a natural topology for a metric space (X, d) is a topology Td induced…
Spacetimes as Topological Spaces, and the Need to Take Methods of General Topology More Seriously
TLDR
Questions are asked in this chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.
On the Causal and Topological Structure of the 2-Dimensional Minkowski Space
A list of all possible causal relations in the two-dimensional Minkowski space M is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are…
On a Duality between Time and Space Cones
We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$, a construction that can be…
Are four dimensions enough? A note on ambient cosmology
In this note, we support that the five-dimensional “ambient cosmology” does not appear to be necessary, neither is required for the scope of avoiding spacetime singularities. This scope can be…

References

SHOWING 1-10 OF 16 REFERENCES
On the possibility of singularities on the ambient boundary
The order horismos induces the Zeeman Z topology, which is coarser than the Fine Zeeman Topology F. The causal curves in a spacetime under Z are piecewise null. F is considered to be the most…
Zeeman topologies on space-times of general relativity theory
AbstractIn 1964 Zeeman published a paper showing [independently of Alexandrov (1953)] that the causal structure of the light cones on Minkowski spaceM determines the linear structure ofM. This…
On the Orderability Problem and the Interval Topology
The class of LOTS (linearly ordered topological spaces, i.e. spaces equipped with a topology generated by a linear order) contains many important spaces, like the set of real numbers, the set of…
Topology of the ambient boundary and the convergence of causal curves
We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be…
A new topology for curved space–time which incorporates the causal, differential, and conformal structures
A new topology is proposed for strongly causal space–times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal,…
The causal order on the ambient boundary
We analyse the causal structure of the ambient boundary, the conformal infinity of the ambient (Poincar\'e) metric. Using topological tools we show that the only causal relation compatible with the…
A Compendium of Continuous Lattices
O. A Primer of Complete Lattices.- 1. Generalities and notation.- 2. Complete lattices.- 3. Galois connections.- 4. Meet-continuous lattices.- I. Lattice Theory of Continuous Lattices.- 1. The…
Causality Implies the Lorentz Group
Causality is represented by a partial ordering on Minkowski space, and the group of all automorphisms that preserve this partial ordering is shown to be generated by the inhomogeneous Lorentz group…
On the structure of causal spaces
The paper examines the structure obtained by abstracting from the conventional (manifold) representation of relativistic space-time the concept of an event-set equipped with two partial orderings,…
Techniques of Differential Topology in Relativity
Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
...
...