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Geometry of interactions in ghost-free bimetric theory
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)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 [en]
Modified gravity, Interacting spin-2 fields, Bimetric theory, Massive gravity
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-148438OAI: oai:DiVA.org:su-148438DiVA: diva2:1152401
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
List of papers
1. On the local structure of spacetime in ghost-free bimetric theory and massive gravity
Open this publication in new window or tab >>On the local structure of spacetime in ghost-free bimetric theory and massive gravity
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.

Keyword
Modied gravity, Interacting spin-2 elds, Bimetric theory, Massive gravity
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-148436 (URN)
Available from: 2017-10-24 Created: 2017-10-24 Last updated: 2017-11-21
2. On Birkhoff's theorem in ghost-free bimetric theory
Open this publication in new window or tab >>On Birkhoff's theorem in ghost-free bimetric theory
2017 (English)In: Article in journal (Refereed) Submitted
Abstract [en]

We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. Besides not being asymptotically flat, the found solutions are nonstationary admitting only three global spacelike Killing vector fields which are the generators of spatial rotations. Hence, these are spherically symmetric bimetric vacuum solutions with the minimal number of isometries. The absence of staticity formally disproves an analogue statement to Birkhoff's theorem in the ghost-free bimetric theory which would state that a spherically symmetric solution is necessarily static in empty space.

Keyword
Modified gravity, Ghost-free bimetric theory, Birkhoff's theorem
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-148437 (URN)
Available from: 2017-10-24 Created: 2017-10-24 Last updated: 2018-01-10
3. Classification and asymptotic structure of black holes in bimetric theory
Open this publication in new window or tab >>Classification and asymptotic structure of black holes in bimetric theory
2017 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 96, no 6, 064003Article in journal (Refereed) Published
Abstract [en]

We study general properties of static and spherically symmetric bidiagonal black holes in Hassan-Rosen bimetric theory by means of a new method. In particular, we explore the behavior of the black hole solutions both at the common Killing horizon and at the large radii. The former study was never done before and leads to a new classification for black holes within the bidiagonal ansatz. The latter study shows that, among the great variety of the black hole solutions, the only solutions converging to Minkowski, anti-de Sitter, and de Sitter spacetimes at large radii are those of general relativity, i.e., the Schwarzschild, Schwarzschild-anti-de Sitter and Schwarzschild-de Sitter solutions. Moreover, we present a proposition, whose validity is not limited to black hole solutions, which establishes the relation between the curvature singularities of the two metrics and the invertibility of their interaction potential.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-146970 (URN)10.1103/PhysRevD.96.064003 (DOI)000409259700003 ()
Available from: 2017-09-19 Created: 2017-09-19 Last updated: 2018-01-10Bibliographically approved

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