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On the local structure of spacetime in ghost-free bimetric theory and massive gravity
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).ORCID iD: 0000-0002-0207-8608
2017 (English)In: Article in journal (Refereed) Submitted
Abstract [en]

The ghost-free bimetric theory describes interactions of gravity with another spin-2 field in terms of two Lorentzian metrics. However, if the two metrics do not admit compatible notions of space and time, the formulation of the initial value problem becomes problematic. Furthermore, the interaction potential in the theory is given in terms of the square root a matrix which is in general nonunique and possibly nonreal. In this paper we prove that the reality of the square root matrix leads to a classification of the allowed configurations of the two metrics in terms of the intersections of their null cones. Then, the equations of motion and general covariance are enough to restrict down the allowed configurations to metrics that admit compatible notions of space and time, and furthermore, lead to a unique definition of the square root matrix. These results ensure that the ghost-free bimetric theory can be defined unambiguously and that the two metrics always admit compatible 3+1 decompositions, at least locally. In particular, these considerations rule out certain solutions of massive gravity with locally Closed Causal Curves, which have been used to argue that the theory is acausal.

Place, publisher, year, edition, pages
2017.
Keyword [en]
Modied gravity, Interacting spin-2 elds, Bimetric theory, Massive gravity
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-148436OAI: oai:DiVA.org:su-148436DiVA: diva2:1152392
Available from: 2017-10-24 Created: 2017-10-24 Last updated: 2017-11-21
In thesis
1. Geometry of interactions in ghost-free bimetric theory
Open this publication in new window or tab >>Geometry of interactions in ghost-free bimetric theory
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The ghost-free bimetric theory is an extension to general relativity where two metric tensors are used instead of one. A priori, the two metrics may not have compatible notions of space and time, which makes the formulation of the initial-value problem problematic. Moreover, the metrics are coupled through a specific ghost-free interaction term that is nonunique and possibly nonreal. We prove that the reality of the bimetric potential leads to a classification of the allowed configurations of the two metrics in terms of the intersections of their null cones. Then, the equations of motion and general covariance are enough to restrict down the allowed configurations to metrics that admit compatible notions of space and time, and furthermore, lead to a unique definition of the potential. This ensures that the ghost-free bimetric theory can be defined unambiguously. In addition, we apply the results on spherically symmetric spacetimes. First, we explore the behavior of the black hole solutions both at the common Killing horizon and at the large radii. The study leads to a new classification for black holes within the bidiagonal ansatz. Finally, we consider the bimetric field equations in vacuum when the two metrics share a single common null direction. We obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. The found solutions are nonstationary and thus nonstatic, which formally disproves an analogous statement to Birkhoff's theorem in the ghost-free bimetric theory.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2017. 42 p.
Keyword
Modified gravity, Interacting spin-2 fields, Bimetric theory, Massive gravity
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-148438 (URN)
Presentation
2017-11-16, FB42, Albanova universitetscentrum, Roslagstullsbacken 21, Stockholm, 14:00 (English)
Opponent
Supervisors
Available from: 2017-12-19 Created: 2017-10-24 Last updated: 2017-12-19Bibliographically approved

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arXiv:1706:07806

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