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1
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Brief accounts of this work are K. V. Kuchař, in Directions in General Relativity I, edited by B. L. Hu, M. P. Ryan, and C. V. Vishveshwara (Cambridge University Press, Cambridge, England, 1993); and
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J. D. Brown and K. V. Kuchař, Phys. Rev. D 51, 5600 (1995). Brief accounts of this work are K. V. Kuchař, in Directions in General Relativity I, edited by B. L. Hu, M. P. Ryan, and C. V. Vishveshwara (Cambridge University Press, Cambridge, England, 1993); and
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Phys. Rev. D
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Brown, J.D.1
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Proceedings of the Cornelius Lanczos Centenary Conference, edited by J. D. Brown, M. T. Chu, D. C. Ellison, and R. J. Plemmons (SIAM, Philadelphia, 1994)
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J. D. Brown, in Proceedings of the Cornelius Lanczos Centenary Conference, edited by J. D. Brown, M. T. Chu, D. C. Ellison, and R. J. Plemmons (SIAM, Philadelphia, 1994).
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Brown, J.D.1
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3
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NATUAS(London)
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P. C. Vaidya, Nature 171, 260 (1953). Here the metric is given in terms of a retarded time coordinate (called by Vaidya a Newtonian time). NATUAS(London)
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Nature
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Vaidya, P.C.1
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4
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Originally, Vaidya found the metric in the Schwarzschild-type coordinates in which it has a more complicated form; see P. C. Vaidya, Curr. Sci. 12, 183 (1943);
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Curr. Sci.
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Vaidya, P.C.1
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0003533113
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edited by S. Deser and K. W. Ford (Prentice Hall, Englewood Cliffs, 1965)
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For a review, see F. A. E. Pirani, in Lectures on General Relativity, edited by S. Deser and K. W. Ford (Prentice Hall, Englewood Cliffs, 1965).
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Lectures on General Relativity
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Pirani, F.A.E.1
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13
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0001163587
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Pfaff's theorem is well described, for example, in Appendix A of B. Schutz, Phys. Rev. D 2, 2762 (1970).
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Phys. Rev. D
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Schutz, B.1
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84917955053
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edited by S. Flügge and C. Truesdell (Springer, Berlin, 1959), Vol. 8]
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J. Serrin, in Handbuch der Physik, edited by S. Flügge and C. Truesdell (Springer, Berlin, 1959), Vol. 8];
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Handbuch der Physik
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Serrin, J.1
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Tam used Clebsch potentials to formulate an action principle for an ideal, charged fluid in the context of special relativity [K. Tam, Can. J. Phys. 44, 2403 (1966)].
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Can. J. Phys.
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Tam, K.1
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17
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Action principles for perfect fluids in general relativity were developed independently by Tam and O'Hanlon [K. Tam and J. O'Hanlon, Nuovo Cimento B 62, 351 (1969)
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Nuovo Cimento B
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O'Hanlon, J.2
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18
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] and by Schutz [B. F. Schutz, Phys. Rev. D 2, 2762 (1970)]. The actions discussed by Tam and O'Hanlon and by Schutz use a minimal set of velocity potentials, which precludes the interpretation of the appropriate potential fields as Lagrangian coordinates for the fluid.
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Phys. Rev. D
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Schutz, B.F.1
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19
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33749562275
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The Hamiltonian form of Schutz's action was developed by Schutz [B. F. Schutz, 4, 3559 (1971)]
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(1971)
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Schutz, B.F.1
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and by Demaret and Moncrief [J. Demaret and V. Moncrief, 21, 2785 (1980)].
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I. Kouletsis, 13, 3085 (1996).
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Kouletsis, I.1
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36
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0642293813
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The form (A1) of the energy-momentum tensor to describe the geometrical optics limit of the neutrino field equations was justified by J. B. Griffiths, 4, 361 (1973), and references therein.
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(1973)
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Griffiths, J.B.1
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166, 1272 (1968);
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GRGVA8
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Interacting gravitational, electromagnetic, and charged scalar fields in the high-frequency limit are discussed by Y. Choquet-Bruhat and A. H. Taub, Gen. Relativ. Gravit. 8, 561 (1977). GRGVA8
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Gen. Relativ. Gravit.
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Choquet-Bruhat, Y.1
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A precise characterization of the high-frequency limit in general relativity was given by C. A. Burnett, J. Math. Phys. (N.Y.) 30, 90 (1989). Burnett proved that there exists an effective energy-momentum tensor [which, in special cases, has the form (A1) appropriate for null dust] that describes high-frequency waves acting as a source of smooth background curvature. He did not need to assume hypersurface orthogonality of (Formula presented).
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J. Math. Phys. (N.Y.)
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Burnett, C.A.1
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41
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for a review, see A. H. Taub, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1979). Whitham's technique averages over a rapidly changing phase directly in a Lagrangian. One thus averages a scalar density (the Hilbert Lagrangian) rather than tensor fields, as in the Brill-Hartle averaging used by Isaacson 22
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M. A. H. MacCallum and A. H. Taub, Commun. Math. Phys. 30, 153 (1973); for a review, see A. H. Taub, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1979). Whitham's technique averages over a rapidly changing phase directly in a Lagrangian. One thus averages a scalar density (the Hilbert Lagrangian) rather than tensor fields, as in the Brill-Hartle averaging used by Isaacson 22.
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Commun. Math. Phys.
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Cambridge University Press, Cambridge, England
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D. Kramer, H. Stephani, M. A. H. MacCallum, and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, England, 1980).
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Exact Solutions of Einstein's Field Equations
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Kramer, D.1
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43
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85038294635
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A. Krasiński, “Physics in an Inhomogeneous Universe,” Copernicus Astronomical Center, Warszaw Report, 1993
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A. Krasiński, “Physics in an Inhomogeneous Universe,” Copernicus Astronomical Center, Warszaw Report, 1993.
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48
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85038324324
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JPHAC5
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Indeed, assuming that the scalar field satisfies the constraint (Formula presented), its energy-momentum tensor assumes the form (A1) after the rescaling (Formula presented). One can easily see that the condition (Formula presented) (which is always satisfied in the geometrical optics approximation) holds exactly for the combined gravitational and massless-scalar plane waves. See W. Z. Chao, J. Phys. A 15, 2429 (1982); and JPHAC5
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J. Phys. A
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Chao, W.Z.1
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49
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0642355095
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M. Halilsoy, Lett. Nuovo Cimento 44, 544 (1985), who considered the collision of such waves.
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Lett. Nuovo Cimento
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Halilsoy, M.1
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T. Damour, 12, 725 (1995).
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Damour, T.1
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53
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85038267341
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These works are mostly related to colliding plane gravitational waves 26
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These works are mostly related to colliding plane gravitational waves 26. Reference 26 also discusses the problem (widely explored in the years 1986–1991) that colliding plane waves accompanied by null dust do not have a unique evolution.
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54
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0011271352
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The problem was introduced by the work of S. Chandrasekhar and C. Xanthopolous, Proc. R. Soc. London A403, 189 (1986), and its discussion led to an understanding that the time evolution of null dust may imply a “transmutation of matter” (here into a stiff fluid) if one does not distinguish different types of null dust representing different types of matter fields.
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(1986)
Proc. R. Soc. London
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Chandrasekhar, S.1
Xanthopolous, C.2
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55
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0000464281
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For a recent work on the collision and interaction of cylindrically symmetric clouds of null dust, see P. S. Letelier and A. Wang, Phys. Rev. D 49, 5105 (1994).
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Phys. Rev. D
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Letelier, P.S.1
Wang, A.2
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56
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21844503002
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For the interaction of outgoing and ingoing spherically symmetric null fluids, see P. R. Holvorcem, P. S. Letelier, and A. Wang, J. Math. Phys. (N.Y.) 36, 3663 (1995).
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J. Math. Phys. (N.Y.)
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Holvorcem, P.R.1
Letelier, P.S.2
Wang, A.3
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57
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0002283076
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A. Papapetrou [in A Random Walk in Relativity and Cosmology, edited by J. Krishna-Rao (Wiley Eastern, New Delhi, 1985)] were the first who noticed that the collapse of spherical shell of null dust may lead to a naked singularity
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Y. Kuroda [Prog. Theor. Phys. 72, 63 (1984)], and A. Papapetrou [in A Random Walk in Relativity and Cosmology, edited by J. Krishna-Rao (Wiley Eastern, New Delhi, 1985)] were the first who noticed that the collapse of spherical shell of null dust may lead to a naked singularity.
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Prog. Theor. Phys.
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Kuroda, Y.1
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W. G. Anderson, P. R. Brady, W. Israel, and S. M. Morsink, 70, 1041 (1993);
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Anderson, W.G.1
Brady, P.R.2
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Morsink, S.M.4
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