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Symmetries and black holes in Hassan–Rosen bimetric theory
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). (CoPS)
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The Hassan–Rosen bimetric theory is an extension of general relativity which considers the interaction between two metric fields defined on the same differentiable manifold. Self-accelerating cosmologies are exact solutions of this theory, and this makes it interesting to explore. We analyze the theory and see if it can provide other physically consistent solutions.

Despite the effort put in studying the theory in recent years, very few exact solutions are known in the literature, and the majority are equivalent to those of general relativity. A valuable approach to try to simplify the field equations and find exact solutions is to impose some spacetime symmetry on the system, e.g., spherical symmetry.

Our study is concerned with symmetries of spacetimes in Hassan–Rosen bimetric theory. Two metrics being present, we investigate what relations exist between their spacetime symmetries. We focus on the isometries of the metrics and clarify when they are the same.

We apply the results in exploring solutions in the Hassan–Rosen theory. We consider maximally symmetric solutions and black hole solutions, and find a previously unknown class of non-stationary spherically symmetric solutions. The existence of the class of non-stationary spherically symmetric solutions disproof a similar statement to Birkhoff's theorem in the Hassan–Rosen bimetric theory. The study of bidiagonal non-rotating black holes sharing the isometries focuses on their properties both at the shared Killing horizon and far from it.

The thesis is a review of these results, and the relevant papers accompany it.

Place, publisher, year, edition, pages
Stockholm University, 2018.
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-151384OAI: oai:DiVA.org:su-151384DiVA, id: diva2:1172717
Presentation
2018-02-08, FB55, Albanova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
Opponent
Supervisors
Available from: 2018-02-16 Created: 2018-01-10 Last updated: 2018-02-16Bibliographically approved
List of papers
1. On spacetime symmetries and topology in bimetric theories
Open this publication in new window or tab >>On spacetime symmetries and topology in bimetric theories
(English)In: Article in journal (Refereed) Submitted
Abstract [en]

We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-151382 (URN)
Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10
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.

Keywords
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: 2018-03-21
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, article id 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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