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Some exceptional electrovac type D metrics with cosmological constant
Abstract
We investigate all type D solutions of the Einstein–Maxwell equations (with cosmological constant) such that the Debever–Penrose vectors are aligned along the two eigenvectors of the electromagnetic field, in the special case when a direct generalization of the Goldberg–Sachs theorem is not possible. A solution is found which admits no Killing vectors. We also present an extension of the Golberg–Sachs theorem valid for type D metrics.
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“For electrovacuum solutions, R = 4Λ so that α = 0 = β, ε = 1, C = 0, D = 2Λ < 0. We thus uniquely obtain the exceptional Plebański-Hacyan universe [28]”
From Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes (2003) · cites this paper as [28]
In the citing paper
“The case 3 2 Ψ 2 = |Φ 1 | 2 was fully integrated in 35 .In the resulting 'Plebański-Hacyan space-times' k and ℓ are respectively non-geodesic (κ = 0) and geodesic (ν = 0), while both are shear-free (σ = λ = 0) and have vanishing complex divergence (ρ = µ = 0).”
From Algebraically special Einstein–Maxwell fields (2017) · cites this paper as [35]
In the citing paper
“This culminated in the complete integration of the field equations for the Petrov type D doubly aligned non-null Einstein-Maxwell fields, with a possible non-0 cosmological constant:”
From Algebraically special Einstein–Maxwell fields (2017) · cites this paper as [35]
In the citing paper
“Moreover, there also exist more general impulsive waves in the 'truly' exceptional spacetime of [2] with < 0, which is not a direct product spacetime (5).”
From Impulsive waves in electrovac direct product spacetimes with (2002) · cites this paper as [2]
In the citing paper
“Recall that these well-known universes [2][3][4][5][6][7] are either vacuum or contain a uniform electromagnetic field, possibly with a cosmological constant .”
From Impulsive waves in electrovac direct product spacetimes with (2002) · cites this paper as [2]
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Metadata
- Authors
- Plebański, J. F., & Hacyan, S.
- Affiliations
- Centro de Investigación y Estudios Avanzados de I.P.N., A.P. 14-740, México, D.F.
- Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (MX)
- ORCID
- Hacyan, Shahen
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1979-06-01
- Volume
- 20
- Issue
- 6
- Pages
- 1004-1010
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2049037574
- Cited by
- 52
- References
- 7
- Citations by year
- 2026: 4 · 2025: 2 · 2024: 1 · 2022: 3 · 2021: 2 · 2020: 2 · 2019: 2 · 2018: 2 · 2017: 1 · 2016: 6 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 2
- FWCI
- 2.64
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Einstein-Maxwell equations, cosmological constant, Killing vector fields, exact solutions
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