Note on the spacetimes of Szekeres

Beverly K. Berger; Douglas M. Eardley; Donald W. Olson

doi:10.1103/PhysRevD.16.3086

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Note on the spacetimes of Szekeres

Beverly K. Berger^* and Douglas M. Eardley^*

Donald W. Olson^†

Department of Physics, Yale University, New Haven, Connecticut 06520

Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853

^*Work supported in part by National Science Foundation under Grant No. PHY76-82353 and Grant No. GP-36317.
^†Work supported in part by the National Science Foundation under Grant No. AST-75-21153 and Grant No. PHY76-07297, and by a Dr. Chaim Weizmann Postdoctoral Fellowship.

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Phys. Rev. D 16, 3086 – Published 15 November, 1977

DOI: https://doi.org/10.1103/PhysRevD.16.3086

Abstract

We find that the "quasispherical" spacetimes of Szekeres have conformally flat space slices in comoving coordinates. These spacetimes can represent pressureless nonspherical gravitational collapse with no gravitational radiation. We give a restriction on general-relativistic exact solutions for matter with pressure which admit flat comoving slices.

References (22)

P. Szekeres, Commun. Math. Phys. 41, 55 (1975)
P. Szekeres, Phys. Rev. D 12, 2941 (1975)
W. Bonnor, Commun. Math. Phys. 51, 191 (1977)
R. Tolman, Proc. Natl. Acad. Sci. 20, 169 (1934)
H. Bondi, Mon. Not. R. Astron. Soc. 107, 410 (1947)
J. Wainwright, J. Math. Phys. 18, 672 (1977)
E. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962)
W. Bonnor, Nature 263, 308 (1976)
J. W. York, Jr., Phys. Rev. Lett. 26, 1656 (1971)
J. W. York, Jr., Phys. Rev. Lett. 28, 1082 (1972)
D. M. Eardley, Phys. Rev. D 12, 3072 (1975)
E. M. Lifshitz and I. M. Khalatnikov, Advan. Phys. 12, 185 (1963)
D. Eardley, E. Liang, and R. Sachs, J. Math. Phys. 13, 99 (1972)
M. E. Cahill and A. H. Taub, Commun. Math. Phys. 21, 1 (1971)
G. F. R. Ellis, in General Relativity and Cosmology, "Enrico Fermi," Course XLVII, edited by R. K. Sachs (Academic, New York, 1971)
D. A. Szafron (unpublished)
D. A. Szafron and J. Wainwright, University of Waterloo report (unpublished)
J. Melnick and R. Tabensky, J. Math. Phys. 16, 958 (1975)
H. Bondi, M. van den Burg, and A. W. K. Metzner, Proc. R. Soc. London A269, 21 (1962)
R. Sachs, Proc. R. Soc. London A270, 103 (1962)
R. Penrose, Proc. R. Soc. London A284, 159 (1965)
R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962)

[c1] P. Szekeres, Commun. Math. Phys. 41, 55 (1975)

[c2] P. Szekeres, Phys. Rev. D 12, 2941 (1975)

[c3] W. Bonnor, Commun. Math. Phys. 51, 191 (1977)

[c4] R. Tolman, Proc. Natl. Acad. Sci. 20, 169 (1934)

[c5] H. Bondi, Mon. Not. R. Astron. Soc. 107, 410 (1947)

[c6] J. Wainwright, J. Math. Phys. 18, 672 (1977)

[c7] E. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962)

[c8] W. Bonnor, Nature 263, 308 (1976)

[c9] J. W. York, Jr., Phys. Rev. Lett. 26, 1656 (1971)

[c10] J. W. York, Jr., Phys. Rev. Lett. 28, 1082 (1972)

[c11] D. M. Eardley, Phys. Rev. D 12, 3072 (1975)

[c12] E. M. Lifshitz and I. M. Khalatnikov, Advan. Phys. 12, 185 (1963)

[c13] D. Eardley, E. Liang, and R. Sachs, J. Math. Phys. 13, 99 (1972)

[c14] M. E. Cahill and A. H. Taub, Commun. Math. Phys. 21, 1 (1971)

[c15] G. F. R. Ellis, in General Relativity and Cosmology, "Enrico Fermi," Course XLVII, edited by R. K. Sachs (Academic, New York, 1971)

[c16] D. A. Szafron (unpublished)

[c17] D. A. Szafron and J. Wainwright, University of Waterloo report (unpublished)

[c18] J. Melnick and R. Tabensky, J. Math. Phys. 16, 958 (1975)

[c19] H. Bondi, M. van den Burg, and A. W. K. Metzner, Proc. R. Soc. London A269, 21 (1962)

[c20] R. Sachs, Proc. R. Soc. London A270, 103 (1962)

[c21] R. Penrose, Proc. R. Soc. London A284, 159 (1965)

[c22] R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962)

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