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Origin of classical singularities. (English) Zbl 0932.83036

Summary: We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras defined on it. Then we present a generalization of this method consisting in changing from functional (commutative) algebras to noncommutative algebras. By representing such an algebra as a space of operators on a Hilbert space we study the existence and properties of various kinds of singular spacetimes. The results obtained suggest that in the noncommutative regime, supposedly reigning in the Planck era, there is no distinction between singular and non-singular states of the universe, and that classical singularities are produced in the transition process from the noncommutative geometry to the standard spacetime physics.

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
81V25 Other elementary particle theory in quantum theory
83C45 Quantization of the gravitational field
83C65 Methods of noncommutative geometry in general relativity
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[1] Bosshard, B. (19 · Zbl 0324.53023 · doi:10.1007/BF01609123
[2] Buchner, K., Heller, M., Multarzyński, P., and Sasin, W. (1993). A
[3] Chamseddine, A. H., Felder, G., and Fröhlich, J. (19 · Zbl 0818.58008 · doi:10.1007/BF02100059
[4] Connes, A. (1994). Noncommutative Geometry (Academic Press, New York). · Zbl 0818.46076
[5] Connes, A. (19 · Zbl 0881.58009 · doi:10.1007/BF02506388
[6] Connes, A., and Rovelli, C. (199 · Zbl 0821.46086 · doi:10.1088/0264-9381/11/12/007
[7] Ellis, G. F. R., and Schmidt, B. G. · Zbl 0434.53048 · doi:10.1007/BF00759240
[8] Geroch, R. (19 · doi:10.1007/BF01645521
[9] Gruszczak, J., and Heller, M. (1992). A
[10] Gruszczak, J., and Heller, M. (199 · Zbl 0798.58002 · doi:10.1007/BF00673765
[11] Hajac, P. M · Zbl 0863.58006 · doi:10.1063/1.531662
[12] Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge). · Zbl 0265.53054
[13] Heller, M. (199 · Zbl 0749.15017 · doi:10.1007/BF00673258
[14] Heller, M., and Sasin, W. (1991). A
[15] Heller, M., and Sasin, W. · Zbl 0818.58005 · doi:10.1007/BF02105828
[16] Heller, M., and Sasin, W · Zbl 0845.58006 · doi:10.1063/1.530988
[17] Heller, M., and Sasin, W. (1995). A
[18] Heller, M., and Sasin, W · Zbl 0866.58010 · doi:10.1063/1.531733
[19] Heller, M., and Sasin, W. (1997). Ba · doi:10.4064/-41-1-153-161
[20] Heller, M., and Sasin, · Zbl 0959.83030 · doi:10.1016/S0375-9601(98)00824-X
[21] Heller, M., Sasin, W., and Lambert, D · Zbl 0892.58006 · doi:10.1063/1.532186
[22] Heller, M., Sasin, W., Trafny, A., and \.Zekanowski, Z. (1992). A
[23] Isham, C. (198 · Zbl 0696.58047 · doi:10.1088/0264-9381/6/11/007
[24] Johnson, R. A · Zbl 0349.53052 · doi:10.1063/1.523357
[25] Landi, G. (1997). An Introduction to Noncommutative Spaces and Their Geometry (Springer-Verlag, Berlin, Heidelberg). · Zbl 0909.46060
[26] Murphy, G. J. (1990). C*-Algebras and Operator Theory (Academic Press, Boston). · Zbl 0714.46041
[27] Odrzygóźdź, Z. (1996). ”Geometrical Properties of Quasiregular Singularities.” Thesis, Warsaw University of Technology.
[28] Schmidt, B. G. · Zbl 0332.53039 · doi:10.1007/BF00759538
[29] Sikorski, R. (1967). · Zbl 0162.25101 · doi:10.4064/cm-18-1-251-272
[30] Sikorski, R. (1971). · Zbl 0226.53004 · doi:10.4064/cm-24-1-45-79
[31] Sikorski, R. (1972). Introduction to Differential Geometry (Polish Scientific Publishers, Warsaw) [in Polish].
[32] Sitarz, J. (199 · Zbl 0812.53082 · doi:10.1088/0264-9381/11/8/017
[33] Tipler, F. J., Clarke, C. J. S., and Ellis, G. F. R. (1980). In General Relativity and Gravitation, A. Held, ed. (Plenum Press, New York), p 97.
[34] Vickers, J. A. G. (198 · Zbl 0576.53044 · doi:10.1088/0264-9381/2/5/016
[35] Vickers, J. A. G. (198 · Zbl 0609.53051 · doi:10.1088/0264-9381/4/1/004
[36] Vickers, J. A. G. (198 · Zbl 0707.53047 · doi:10.1088/0264-9381/7/5/004
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