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Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions
Abstract
In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a nontwisting null congruence. Specific properties of all nontwisting type N vacuum solutions with cosmological constant Λ (nonexpanding Kundt class and expanding Robinson–Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes “+” and “×,” shifted by π/4, which propagate “on” Minkowski, de Sitter or anti-de Sitter backgrounds. It is also shown that the solutions with Λ>0 may serve as exact demonstrations of the cosmic “no-hair” conjecture in radiative spacetimes with no symmetry.
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“A complete class of non-expanding type N vacuum solutions with (possibly) non-vanishing cosmological constant was found by Ozsváth, Robinson and Rózga [15], and later studied also from a physical point of view [33].”
From Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes (2003) · cites this paper as [33]
In the citing paper
“Note finally (cf. the general analysis in [33]) that the interpretation frame (49) is parallelly transported along the geodesic if and only if (Q/P )ζ = 0 = (Q/P ) ζ .”
From Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes (2003) · cites this paper as [33]
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Citations
Cites
An Approach to Gravitational Radiation by a Method of Spin Coefficients
Newman, E., & Penrose, R. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724257 · Cited by 2,702
Penrose, R., & Rindler, W. (1984) · doi:10.1017/cbo9780511564048 · Cited by 2,172
Research works printed but not linked: 9
- 1999, Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions, J. Math. Phys., 40, 4495, 10.1063/1.532981 · DOI · Paper page
- 1956, On the physical significance of the Riemann tensor, Acta Phys. Pol., 15, 389
- 1957, Invariant formulation of gravitational radiation theory, Phys. Rev., 150, 1089
- 1965, The gravitational compass, J. Math Phys., 6, 1387, 10.1063/1.1704788 · DOI
- 1995, Cosmic no-hair conjecture and black-hole formation: an exact model with gravitational radiation., Phys. Rev. D, 52, 887, 10.1103/PhysRevD.52.887 · DOI
- 1997, Global structure of Robinson–Trautman radiative space–times with cosmological constant, Phys. Rev. D, 55, 1985, 10.1103/PhysRevD.55.1985 · DOI
- 1992, On the strength of a gravitational field, Phys. Lett. A, 163, 7, 10.1016/0375-9601(92)90151-B · DOI
- 1960, Spherical gravitational waves, Phys. Rev. Lett., 4, 431, 10.1103/PhysRevLett.4.431 · DOI
- 1998, Curvature invariants in type N spacetime, Class. Quantum Grav., 15, 1539, 10.1088/0264-9381/15/6/011 · DOI
Cited by
Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes
Podolsk, J., & Ortaggio, M. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/9/307 · Cited by 61
Self-citation
Metadata
- Authors
- Bičák, J., & Podolský, J.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1999-09-01
- Volume
- 40
- Issue
- 9
- Pages
- 4506-4517
- ISSN
- 0022-2488
- 1089-7658
- Cited by
- 52
- References
- 2
- Language
- en
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