Abstract
Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of a singular hypersurface are derived and a specific non-vanishing form for the energy-momentum tensor of the singular hypersurface is obtained. It is shown that matching in the case of de Sitter space in the Lorentzian sector is possible along the boundary with minimum radius but leads to the vanishing of the energy-momentum tensor of the singular hypersurface.
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REFERENCES
Hartle, J. B., and Hawking, S. W. (1983). Phys. Rev. D 28, 2960; Hawking, S. W. (1984). Nucl. Phys. B 239, 257.
Halliwell, J. J., and Hartle, J. B. (1990). Phys. Rev. D 41, 1815.
Gibbons, G. W., and Hartle, J. B. (1990). Phys. Rev. D 42, 2458.
Isham, C. J. (1989). Class. Quantum Grav. 6, 1509.
Horowitz, G. T. (1991). Class. Quantum Grav. 8, 587.
Gibbons, G. W., and Hawking, S. W. (1992). Commun. Math. Phys. 148, 345.
Sakharov, A. D. (1984). Sov. Phys. JETP 60, 214; see also Al'tshuler, B. L., and Barvinsky, A. O. (1996). Phys. Uspekhi 39, 429.
Ellis, G. F. R., Sumruk, A., Coule, D., and Hellaby, C. (1992). Class. Quantum Grav. 9, 1535; see also Ellis, G. F. R., et al. (1997). Gen. Rel. Grav. 29, 591.
Ellis, G. F. R. (1992). Gen. Rel. Grav. 24, 1047.
Hayward, S. A. (1992). Class. Quantum Grav. 9, 1851.
Hayward, S. A. (1993). Class. Quantum Grav. 10, L7; id. (1994). Class. Quantum Grav. 11, L87.
Dereli, T., and Tucker, R. W. (1993). Class. Quantum Grav. 10, 365.
Kossowski, M., and Kriele, M. (1993). Class. Quantum Grav. 10, 1157; id. (1993). Class. Quantum Grav. 10, 2363.
Hayward, S. A. (1995). Preprint gr-qc/9509052; id. (1996). Preprint gr-qc/9606044.
Hellaby, C., and Dray, T. (1994). Phys. Rev. D 49, 5096.
Kriele, M., and Martin, J. (1995). Class. Quantum Grav. 12, 503.
Martin, J. (1994). Phys. Rev. D 49, 5086; id. (1995). Phys. Rev. D 52, 6708.
Hayward, S. A. (1995). Phys. Rev. D 52, 7331.
Hellaby, C., and Dray, T. (1995). Phys. Rev. D 52, 7333.
Dray, T., Manogue, C. A., and Tucker, R. W. (1991). Gen. Rel. Grav. 23, 967; id. (1993). Phys. Rev. D 48, 2587; Dereli, T., Önder, M., and Tucker, R. (1993). Class. Quantum Grav. 10, 1425; Egusquiza, I. L. (1995). Class. Quantum Grav. 12, L89; Maia, M. D., and Monte E. M. (1995). Preprint gr-qc/9501031; Hayward, S. A. (1995). Preprint gr-qc/9502001; Alty, L. J., and Fewster, C. J. (1995). Preprint gr-qc/9501026; Dray, T., Manogue, C. A., and Tucker, R. W. (1995). Preprint grqc/9501034; Kriele, M. (1996). Preprint gr-qc/9610016; Dray, T. (1996). J. Math. Phys. 37, 5627; Iliev, B. Z. (1998). Preprints gr-qc/9802057, gr-qc/9802058.
Khorrami, M., and Mansouri, R. (1991). J. Math. Phys. 35, 951.
Hartley, D., et al. (1997). Preprint gr-qc/9701046; Dray, T. (1997). Preprint grqc/97010717.
Mansouri, R., and Khorrami, M. (1996). J. Math. Phys. 37, 5672.
Colombeau, J. F. (1992). Multiplication of Distributions (LNM 1532, Springer-Verlag, Berlin).
Oberguggenberger, M. (1992). Multiplication of Distributions and Applications to PDEs (Longman, London).
Balasin, H. (1996). Preprint gr-qc/9610017.
Clark, C., Vickers, J., and Wilson, J. (1996). Class. Quantum Grav. 13, 2485.
Wilson, J. (1997). Preprint gr-qc/9705032.
Kanwal, R. M. (1983). Generalized Functions: Theory and Technique (Academic Press, New York).
Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).
Hayward, S. A. (1993). Preprint gr-qc/9303034 v2.
Dray, T. (1996). J. Math. Phys. 37, 5627.
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Mansouri, R., Nozari, K. A New Distributional Approach to Signature Change. General Relativity and Gravitation 32, 253–269 (2000). https://doi.org/10.1023/A:1001991609020
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DOI: https://doi.org/10.1023/A:1001991609020