The Chevreton tensor and Einstein–Maxwell spacetimes conformal to Einstein spaces

Bergqvist, Göran; Eriksson, Ingemar

doi:10.1088/0264-9381/24/13/018

Cited by 5 publications

(10 citation statements)

References 29 publications

(59 reference statements)

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“…JK would like to thank Pawe l Nurowski for suggesting this research problem and pointing out the reference [20]. The research leading to these results has received funding from the Norwegian Financial Mechanism 2014-2021, project registration number UMO-2019/34/H/ST1/00636.…”

Section: Acknowledgementsmentioning

confidence: 97%

“…Following the discussion at the end of Section 4, we present an example of electrovacuum spacetimes that admit regular conformal Bach equation. This is based on the analysis of the Chevreton tensor given in [20]. As the equations simplify greatly with the use of the spinorial formalism, we will employ it here.…”

Section: Matching Conditions For the Conformal Boundary Between Aeonsmentioning

confidence: 99%

“…Hence, in order for the conformal Bach equation to be regular, an assumption has to be made about the Maxwell spinor. The result in [20] showed that the simple condition q ∇ CC 1 q φ AB q ∇ CC 1 q φ 1 A 1 B 1 " 0 restricts the spacetime to the Petrov type N or O and vanishing cosmological constant, so in that case the Bach tensor vanishes.…”

mentioning

confidence: 99%

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The Bach equation and the matching of spacetimes in the Conformal Cyclic Cosmology models

Kopiński¹,

Kroon²

2022

Preprint

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We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has regular conformal Bach tensor will be discussed in the appendix.

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Section: Acknowledgementsmentioning

confidence: 97%

Section: Matching Conditions For the Conformal Boundary Between Aeonsmentioning

confidence: 99%

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The Bach equation and the matching of spacetimes in the Conformal Cyclic Cosmology models

Kopiński¹,

Kroon²

2022

Preprint

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“…Hence, in order for the conformal Bach equation to be regular, an assumption has to be made about the Maxwell spinor. The result in [26] showed that the simple condition q ∇ CC 1 q φ AB q ∇ CC 1 q φ 1 A 1 B 1 " 0 restricts the spacetime to the Petrov type N or O and vanishing cosmological constant, so in that case the Bach tensor vanishes.…”

Section: A Initial Values Of the (Electro)magnetic Fieldsmentioning

confidence: 99%

Bach equation and the matching of spacetimes in conformal cyclic cosmology models

Kopiński

Kroon²

2022

Phys. Rev. D

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We consider the problem of matching two spacetimes, the previous and present aeons, in the conformal cyclic cosmology model. The common boundary between them inherits two sets of constraints -one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffices to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach-type equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has a regular conformal Bach tensor will be discussed in the Appendix.

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“…However, vanishing of the Bach tensor is not a sufficient condition for a spacetime to be conformally related to an Einstein spacetime [14]. Indeed, explicit examples of spacetimes with vanishing Bach tensor which are not conformal to Einstein spacetimes are known [15,16]. One can employ (9) to construct new exact solutions to quadratic gravity with arbitrary nonzero parameters α ′ , β ′ , γ ′ but a special value of the cosmological constant…”

Section: Conformally Kundt Solutions To Quadratic Gravitymentioning

confidence: 99%

Exact solutions to quadratic gravity

et al. 2017

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Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime.Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

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The Chevreton tensor and Einstein–Maxwell spacetimes conformal to Einstein spaces

Cited by 5 publications

References 29 publications

The Bach equation and the matching of spacetimes in the Conformal Cyclic Cosmology models

The Bach equation and the matching of spacetimes in the Conformal Cyclic Cosmology models

Bach equation and the matching of spacetimes in conformal cyclic cosmology models

Exact solutions to quadratic gravity

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