The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
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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In the citing paper
“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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Citations
Cites
Rotating, charged, and uniformly accelerating mass in general relativity
Plebanski, J. F., & Demianski, M. (1976) · Annals of Physics · doi:10.1016/0003-4916(76)90240-2 · Cited by 677
Uniform Electromagnetic Field in the Theory of General Relativity
Bertotti, B. (1959) · Physical Review · doi:10.1103/physrev.116.1331 · Cited by 411
Solutions of the Einstein and Einstein-Maxwell Equations
Debney, G. C., Kerr, R. P., & Schild, A. (1969) · Journal of Mathematical Physics · doi:10.1063/1.1664769 · Cited by 375
A class of solutions of Einstein-Maxwell equations
Plebanski, J. F. (1975) · Annals of Physics · doi:10.1016/0003-4916(75)90145-1 · Cited by 179
On a quadratic first integral for the charged particle orbits in the charged Kerr solution
Hughston, L. P., Penrose, R., Sommers, P., & Walker, M. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01645517 · Cited by 112
Complex relativity and double KS metrics
Plebanski, J. F., & Schild, A. (1976) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02726281 · Cited by 36
Weir, G., & Kerr, R. P. (1977) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1977.0085 · Cited by 21
Research works printed but not linked: 5
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- 1977, Proc. R. Soc. London Ser. A, 335, 31
- 1959, Bull. Acad. Pol. Sci. Sec. Math. Phys., 7, 35
- 1966, Proceedings of Symposia in Applied Mathematics, 17, 199
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Cited by
Duality rotations and type D solutions to Einstein equations with nonlinear electromagnetic sources
Humberto Salazar, I., Alberto García, D., & Plebanski, J. F. (1987) · Journal of Mathematical Physics · doi:10.1063/1.527430 · Cited by 229
Flores-Alfonso, D., Gonzalez-Morales, B. A., Linares, R., & Maceda, M. (2020) · Physics Letters B · doi:10.1016/j.physletb.2020.136011 · Cited by 110
Nariai, Bertotti-Robinson, and anti-Nariai solutions in higher dimensions
Cardoso, V., Dias, Ó. J. C., & Lemos, J. P. S. (2004) · Physical Review D · doi:10.1103/physrevd.70.024002 · Cited by 107
Debever, R., Kamran, N., & McLenaghan, R. G. (1984) · Journal of Mathematical Physics · doi:10.1063/1.526386 · Cited by 66
Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes
Podolsk, J., & Ortaggio, M. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/9/307 · Cited by 61
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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- Plebański, J. F., & Hacyan, S. (1979). Some exceptional electrovac type D metrics with cosmological constant. Journal of Mathematical Physics. https://doi.org/10.1063/1.524174
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