Behavior of Einstein-Rosen waves at null infinity

Abhay Ashtekar; Jiří Bičák; Bernd G. Schmidt

doi:10.1103/PhysRevD.55.687

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Behavior of Einstein-Rosen waves at null infinity

Abhay Ashtekar

Jiří Bičák

Bernd G. Schmidt

Center for Gravitational Physics and Geometry, Department of Physics, Penn State, University Park, Pennsylvania 16802

Department of Theoretical Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic

Max-Planck-Institut für Gravitationsphysik, Schlaatzweg 1, 14473 Potsdam, Germany

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Phys. Rev. D 55, 687 – Published 15 January, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.687

Abstract

The asymptotic behavior of Einstein-Rosen waves at null infinity in four dimensions is investigated in all directions by exploiting the relation between the four-dimensional space-time and the three-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is better than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be understood most clearly from the three-dimensional perspective.

References (17)

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J. Stachel,J. Math. Phys. (N.Y.), 7 1321 (1966).
J. Winicour,Found. Phys., 15 605 (1985).
Omitted end note.
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D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, England, 1980).
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J. Bicák,Proc. R. Soc. London, A302 201 (1968).
J. Bicák andB. G. Schmidt,Class. Quantum Grav., 6 1547 (1989).
J. Bicák andB. G. Schmidt,J. Math. Phys. (N.Y.), 25 600 (1984).
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[c1] A. Ashtekar, J. Bicák and B. G. Schmidt, preceding paper, Phys. Rev. D 55, 669 (1997).

[c2] J. Stachel,J. Math. Phys. (N.Y.), 7 1321 (1966).

[c3] J. Winicour,Found. Phys., 15 605 (1985).

[c4] Omitted end note.

[c5] J. Bicák andB. G. Schmidt,Phys. Rev. D, 40 1827 (1989).

[c6] D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, England, 1980).

[c7] P. Jordan,J. Ehlers, andW. Kundt,Akad. Wiss. Lit. Mainz Abh. Math. Naturwiss. Kl.Nr 2 (1960).

[c8] G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

[c9] R. Penrose,Phys. Rev. Lett., 10 66 (1963); Proc. R. Soc. London, A284 159 (1965).

[c10] H. Bondi,M. van der Burg, andA. Metzner,Proc. R. Soc. London, A269 21 (1962).

[c11] J. Bicák,Proc. R. Soc. London, A302 201 (1968).

[c12] J. Bicák andB. G. Schmidt,Class. Quantum Grav., 6 1547 (1989).

[c13] J. Bicák andB. G. Schmidt,J. Math. Phys. (N.Y.), 25 600 (1984).

[c14] J. Weber andJ. Wheeler,Rev. Mod. Phys., 29 509 (1957).

[c15] W. B. Bonnor,J. Math. Mech., 6 203 (1957).

[c16] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).

[c17] M. Carmeli, Classical Fields: General Relativity and Gauge Theory (Wiley, New York, 1982).

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