Consequences of the noncompactness of the Lorentz group
作者： Hans-Jurgen Schmidt
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摘要: The following four statements for indefinitemetrics of Lorentz signature do not possess an analogousstatement in the definite Euclidean case: (1)All curvature invariants a gravitational wave vanish, spite fact that itrepresents nonflat spacetime. (2) eigennullframecomponents tensor (the Cartan“scalars”) represent curvaturescalars. (3) topology Minkowskispacetime doesnot possessa basis composedofLorentzinvariant neighborhoods. (4) There are pointsin de Sitter spacetime which cannot be joined toeach other by any geodesic. We show these fourstatements all follow from noncompactness theLorentz group. conclude popular (and oftenuseful) imaginary-coordinate rotation to Lorentzian (called Wick rotation) isnot isomorphism.
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Garry Ludwig, S. Brian Edgar, Integration in the GHP formalism I: A coordinate approach with applications to twisting type N spaces General Relativity and Gravitation. ,vol. 28, pp. 707- 733 ,(1996) , 10.1007/BF02104837
Stephen W. Hawking, George Francis Rayner Ellis, The Large Scale Structure of Space-Time ,(1973)
Rainer Schimming, RIEMANNsche Räume mit ebenfrontiger und mit ebener Symmetrie Mathematische Nachrichten. ,vol. 59, pp. 129- 162 ,(1974) , 10.1002/MANA.19740590111
R. Geroch, A. Held, R. Penrose, A space‐time calculus based on pairs of null directions Journal of Mathematical Physics. ,vol. 14, pp. 874- 881 ,(1973) , 10.1063/1.1666410
Hans-JÜRgen Schmidt, On the de Sitter space-time - the geometric foundation of inflationary cosmology. Protein Science. ,vol. 41, pp. 179- 199 ,(1993) , 10.1002/PROP.2190410302
P.J. Hawking, S.W., King, A.R., McCarthy, None, A new topology for curved space–time which incorporates the causal, differential, and conformal structures Journal of Mathematical Physics. ,vol. 17, pp. 174- 181 ,(1976) , 10.1063/1.522874
D. T. Fullwood, A new topology on space‐time Journal of Mathematical Physics. ,vol. 33, pp. 2232- 2241 ,(1992) , 10.1063/1.529644