What is the geometry of superspace?
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The configuration space of general relativity, called superspace or the space of three-geometries, inherits certain geometric structures from the Wheeler-DeWitt metric on the larger space of Riemannian metrics. We analytically investigate the signature properties of the particular geometric structure associated with the choice of constant lapse function. We point out that this metric has rather special properties and generically suffers from signature changes.
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The Wheeler-DeWitt equation is a hyperbolic differential equation involving the scale factor, and it remains hyperbolic after small perturbations of homogeneous metrics.
“This equation is a hyperbolic differential equation involving the scale factor of the universe, which plays a role analogous to a time variable.It remains hyperbolic after small perturbations of the homogeneous metrics [3].”
From Loop quantum cosmology: I. Kinematics (2000) · cites this paper as [3]
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- Authors
- Giulini, D.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Giulini, Domenico
- ORCID
- Giulini, Domenico
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1995-05-15
- Volume
- 51
- Issue
- 10
- Pages
- 5630-5635
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2045353638
- Cited by
- 74
- References
- 12
- Citations by year
- 2026: 2 · 2025: 16 · 2024: 1 · 2023: 1 · 2022: 3 · 2021: 3 · 2020: 3 · 2019: 2 · 2018: 1 · 2017: 2 · 2016: 3 · 2015: 1 · 2014: 2
- FWCI
- 2.83
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- superspace, signature change, Riemannian metrics, quantum gravity, Hamiltonian constraint
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