Research PapersNo Access

Null hypersurfaces in de Sitter and anti-de Sitter cosmologies

School of Physics, University College Dublin, Belfield, Dublin 4, Ireland

https://doi.org/10.1142/S0218271818500451Cited by:4 (Source: Crossref)

Abstract

The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in spacetimes of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision spacetime is a solution of Einstein’s field equations with a cosmological constant, and the second originated in the generalization of plane fronted gravitational waves with parallel rays to include a cosmological constant.

Keywords:

PACS: 04.40.Nr, 04.30.Nk

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References

1. C. Barrabès and P. A. Hogan, Phys. Rev. D 92 (2015) 044032. Crossref, Web of Science, ADS, Google Scholar
2. I. Ozsváth, I. Robinson and K. Rózga, J. Math. Phys. 26 (1985) 1755. Crossref, Web of Science, ADS, Google Scholar
3. H. V. Tran, The geometry of plane waves in spaces of constant curvature, Ph.D. thesis, University of Texas, Dallas (1988). Google Scholar
4. I. Robinson, Internal Report, University of Texas, Dallas (1983). Google Scholar
5. C. Barrabès and P. A. Hogan, Advanced General Relativity: Gravity Waves, Spinning Particles, and Black Holes, International Series of Monographs on Physics, No. 160 (Oxford University Press, Oxford, 2013). Crossref, Google Scholar
6. E. I. Schucking and J.-Z. Wang, Gravitation and Geometry, eds. W. Rindler and A. Trautman (Bibliopolis, Naples, 1987). Google Scholar
7. E. Schrödinger, Expanding Universes (Cambridge University Press, Cambridge, 1956). Crossref, Google Scholar
8. J. L. Synge, Relativity: The General Theory (North-Holland Publishing Company, Amsterdam, 1966). Google Scholar
9. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973). Crossref, Google Scholar
10. J. Podolsky and O. Hruska, arXiv:1703.01367v1 [gr-qc]. Google Scholar
11. R. Penrose, General Relativity: Papers in Honour of J. L. Synge (Clarendon Press, Oxford, 1972). Google Scholar
12. I. Robinson and A. Trautman, J. Math. Phys. 24 (1983) 1425. Crossref, Web of Science, ADS, Google Scholar
13. P. A. Hogan, Null hyperplanes in space-times of constant curvature, invited talk in Mathematical Physics and General Relativity Symposium in Honour of Ivor Robinson, University of Texas, Dallas, May 7–9, 2017, (http://www.utdallas.edu/mkd034000/GenRelConfUTD/). Google Scholar