On a duality between Time and Space Cones
Keywords:
causality, chronology, chorology, Minkowski space, time cone, space cone, weak interval topology, dualityAbstract
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 extended to any curved spacetime, and we discuss its geometrical as well as its topological implications.References
R. Penrose, Techniques of Differential Topology in Relativity, CBMS-NSF Regional Conference Series in Applied Mathematics, 1972.
Gierz, Gerhard and Hofmann, Karl Heinrich and Keimel, Klaus
and Lawson, Jimmie D. and Mislove, Michael W. and Scott, Dana S. A compendium of continuous lattices. Springer-Verlag, 1980.
E.C. Zeeman, The Topology of Minkowski Space,
Topology, Vol. 6, 161-170(1967).
Ignatios Antoniadis, Spiros Cotsakis and Kyriakos Papadopoulos, The Causal Order on the Ambient Boundary, Mod. Phys. Lett. A, Vol 31, Issue 20, 2016.
G.M. Reed, The intersection topology w.r.t. the real line and the countable ordinals (Trans. Am. Math. Society, Vol. 297, No 2, 1986, pp 509-520).
Roger Penrose, The Road to Reality: a complete guide to the laws of the universe, Vintage Books, 2007 edition.
Hawking, S. W. and King, A. R. and McCarthy, P. J. (1976),A new topology for curved space–time which incorporates the causal, differential, and conformal structures. Journal of Mathematical Physics, 17 (2). pp. 174-181.
Kyriakos B. Papadopoulos, Santanu Acharjee and Basil K. Papadopoulos, The Order On the Light Cone and Its Induced Topology, International Journal of Geometric Methods in Modern Physics 15, 1850069 (2018).
Kyriakos B. Papadopoulos and Basil K. Papadopoulos, On Two Topologies that were suggested by Zeeman,
Mathematical Methods in the Applied Sciences, Vol 41, Issue 17, 2018.
S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973.
