Asymptotic behaviour in polarized and half-polarized U (1) symmetric vacuum spacetimes
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We use the Fuchsian algorithm to study the behaviour near the singularity of certain families of U (1) symmetric solutions of the vacuum Einstein equations (with the U (1) isometry group acting spatially). We consider an analytic family of polarized solutions with the maximum number of arbitrary functions consistent with the polarization condition (one of the ‘gravitational degrees of freedom’ is turned off) and show that all members of this family are asymptotically velocity term dominated (AVTD) as one approaches the singularity. We show that the same AVTD behaviour holds for a family of ‘half-polarized’ solutions, which is defined by adding one extra arbitrary function to those characterizing the polarized solutions. (The full set of nonpolarized solutions involves two extra arbitrary functions.) Using SL (2, R ) Geroch transformations, we produce a further class of U (1) symmetric solutions with AVTD behaviour. We begin to address the issue of whether AVTD behaviour is independent of the choice of time foliation by showing that indeed AVTD behaviour is seen for a wide class of choices of harmonic time in the polarized and half-polarized ( U (1) symmetric vacuum) solutions discussed here.
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Using the sub- and super-solution technique, there is a unique solution φ[γ,kTT,τ] of the Lichnerowicz equation.
“Using the sub and super solution technique [38, 40], it is established that there is a unique solution φ [ γ, k TT , τ ] of the Lichnerowicz equation.”
From Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space (2023) · cites this paper as [38]
The Asymptotic Constraint Equations section (p. 28) says that the Einstein superHamiltonian constraint is a nonlinear elliptic equation for the conformal factor ψ and that it has a unique solution for nonzero constant mean curvature and generic conformal data. It does not identify this as a Lichnerowicz equation for φ[γ,kTT,τ] or say that the result is established using sub- and super-solutions; its stated conditions also limit the uniqueness claim. (LLM, conf=0.86)
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Gowdy, R. H. (1974) · Annals of Physics · doi:10.1016/0003-4916(74)90384-4 · Cited by 330 · see citing works
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Research works printed but not linked: 1
- [16][16] H. Ringstrom, 'The Bianchi IX attractor', Ann Inst. H. Poinc. 2, 405500 (2001). -
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Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space
Mondal, P. (2023) · Journal of Mathematical Physics · doi:10.1063/5.0136631 · Cited by 1 · see citing works
- Authors
- Isenberg, J., & Moncrief, V.
- Affiliations
- University of Oregon (US)
- Yale University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2002-10-15
- Volume
- 19
- Issue
- 21
- Pages
- 5361-5386
- ISSN
- 0264-9381 (ISSN-L)
- OpenAlex
- W2034591814
- Cited by
- 93
- References
- 1
- Citations by year
- 2025: 5 · 2024: 2 · 2023: 4 · 2022: 3 · 2021: 2 · 2020: 2 · 2019: 5 · 2018: 2 · 2017: 2 · 2016: 3 · 2015: 3 · 2014: 4 · 2013: 2
- FWCI
- 1.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Yale University
- 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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- vacuum Einstein equations, spacetime singularities
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