Zeeman-Like Topologies in Special and General Theory of Relativity

This is a short review article in which we discuss and summarize the works of various researchers over past four decades on Zeeman topology and Zeeman-like topologies, which occur in special and general theory of relativity. We also discuss various properties and inter-relationship of these topologies.

[1]  Transformations of strongly causal space–times preserving null geodesics , 1998 .

[2]  R. V. Saraykar,et al.  Causal cones, cone preserving transformations and causal structure in special and general relativity , 2012, 1208.4580.

[3]  S. Nanda.  Weaker Versions of Zeeman's Conjectures on Topologies for Minkowski Space , 1972 .

[4]  Jürgen Ehlers,et al.  General relativity and kinetic theory. , 1971 .

[5]  Properties of the λ topology , 1970 .

[6]  R. Z. Domiaty.  On bijections of Lorentz manifolds, which leave the class of spacelike paths invariant , 1985 .

[7]  Jan Peleska.  A characterization for isometries and conformal mappings of pseudo-Riemannian manifolds , 1984 .

[8]  R. Z. Domiaty.  Topologies for Lorentz manifolds: The space topology , 1985 .

[9]  E. C. Zeeman,et al.  The topology of Minkowski space , 1967 .

[10]  R. Sorkin,et al.  A causal order for spacetimes with Lorentzian metrics: proof of compactness of the space of causal curves , 1995, gr-qc/9508018.

[11]  Some results on the Zeeman topology , 2007, 0704.2933.

[12]  D. Dieks.  The Ontology Of Spacetime , 2006 .

[13]  Simple connectedness of spacetime in the path topology , 2010 .

[14]  On Zeeman Topology in Kaluza-Klein and Gauge Theories , 2005, math-ph/0504071.

[15]  P. Joshi.  Global Aspects in Gravitation and Cosmology , 1994 .

[16]  Gunjan Agrawal,et al.  t-topology on the n-dimensional Minkowski space , 2009 .

[17]  Andrew King,et al.  A new topology for curved space–time which incorporates the causal, differential, and conformal structures , 1976 .

[18]  S. Nanda.  Topology for Minkowski Space , 1971 .

[19]  J. Mashford.  A nonmanifold theory of space–time , 1981 .

[20]  Zeeman-Göbel Topologies , 1988, The British Journal for the Philosophy of Science.

[21]  D. Malament.  The class of continuous timelike curves determines the topology of spacetime , 1977 .

[22]  R. Sachs,et al.  Causal boundaries for general relativistic space‐times , 1974 .

[23]  K-Causality Coincides with Stable Causality , 2008, 0809.1214.

[24]  Do-Hyung Kim.  The path topology and the causal completion , 2006 .

[25]  D. Fullwood.  A new topology on space‐time , 1992 .

[26]  R. Penrose.  Techniques of Differential Topology in Relativity , 1972 .

[27]  Zeeman topologies on space-times of general relativity theory , 1976 .

[28]  J. Senovilla,et al.  Causal relationship: a new tool for the causal characterization of Lorentzian manifolds , 2002, gr-qc/0207110.

[29]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.