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Cited by 77Relativity and Gravitational TheoryCosmology and Gravitation TheoriesPulsars and Gravitational Waves Research

The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.

Structure of the singularities produced by colliding plane waves

Yurtsever, Ulvi·1988·Physical Review D
DOI 10.1103/physrevd.38.1706
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Abstract

When gravitational plane waves propagating and colliding in an otherwise flat background interact, they produce spacetime singularities. If the colliding waves have parallel (linear) polarizations, the mathematical analysis of the field equations in the interaction region is especially simple. Using the formulation of these field equations previously given by Szekeres, we analyze the asymptotic structure of a general colliding parallel-polarized plane-wave solution near the singularity. We show that the metric is asymptotic to an inhomogeneous Kasner solution as the singularity is approached. We give explicit expressions which relate the asymptotic Kasner exponents along the singularity to the initial data posed along the wave fronts of the incoming, colliding plane waves. It becomes clear from these expressions that for specific choices of initial data the curvature singularity created by the colliding waves degenerates to a coordinate singularity, and that a nonsingular Killing-Cauchy horizon is thereby obtained. Our equations prove that these horizons are unstable in the full nonlinear theory against small but generic perturbations of the initial data, and that in a very precise sense, ``generic'' initial data always produce all-embracing, spacelike curvature singularities without Killing-Cauchy horizons. We give several examples of exact solutions which illustrate some of the asymptotic singularity structures that are discussed in the paper. In particular, we construct a new family of exact colliding parallel-polarized plane-wave solutions, which create Killing-Cauchy horizons instead of a spacelike curvature singularity. The maximal analytic extension of one of these solutions across its Killing-Cauchy horizon results in a colliding plane-wave spacetime, in which a Schwarzschild black hole is created out of the collision between two plane-symmetric sandwich waves propagating in a cylindrical universe.

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Crossref · 10.1103/physrevd.38.1706

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39 of 39 references verified0 citation errors · 0 not checkable

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Show all 38 references

Research works printed but not linked: 4

  1. V. A. Belinsky, 1970, Sov. Phys. JETP, 30, 1174
  2. P. R. Garabedian, 1967, Partial Differential Equations
  3. F. J. Tipler, 1979, Einstein Centenary Volume
  4. K. Yosida, 1985, Functional Analysis

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Metadata

Authors
Yurtsever, U.
Affiliations
California Institute of Technology (US)
Corresponding author
Yurtsever, Ulvi
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1988-09-15
Volume
38
Issue
6
Pages
1706-1730
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.38.1706
OpenAlex
W1985117253
Semantic Scholar
9b565217ffddd120894d0c6f9d329ad04640272d
Cited by
75
References
38
Citations by year
2026: 1 · 2025: 1 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 1 · 2020: 1 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 3 · 2015: 2 · 2014: 1 · 2013: 1
FWCI
7.97
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
Keywords
colliding plane waves, spacetime singularities, Kasner solutions, asymptotic structure, coordinate singularities, curvature singularity

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