Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Covariant BSSN formulation in bimetric relativity
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).
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).ORCID iD: 0000-0003-0243-1229
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
2020 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 37, no 2, article id 025013Article in journal (Refereed) Published
Abstract [en]

Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations  as a well-posed problem. In general relativity, under certain assumptions, the covariant BSSN formulation is a strongly hyperbolic formulation of the Einstein equations, hence its Cauchy problem is well-posed. In this paper, we establish the covariant BSSN formulation of the bimetric field equations. It shares many features with the corresponding formulation in general relativity, but there are a few fundamental differences between them. Some of these differences depend on the gauge choice and alter the hyperbolic structure of the system of partial differential equations compared to general relativity. Accordingly, the strong hyperbolicity of the system cannot be claimed yet, under the same assumptions as in general relativity. In the paper, we stress the differences compared with general relativity and state the main issues that should be tackled next, to draw a roadmap towards numerical bimetric relativity.

Place, publisher, year, edition, pages
2020. Vol. 37, no 2, article id 025013
Keywords [en]
ghost-free bimetric theory, Hassan–Rosen bimetric theory, bimetric relativity, BSSN formulation, numerical relativity
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-178348DOI: 10.1088/1361-6382/ab56fcOAI: oai:DiVA.org:su-178348DiVA, id: diva2:1388476
Available from: 2020-01-24 Created: 2020-01-24 Last updated: 2020-02-06Bibliographically approved
In thesis
1. Theoretical and numerical bimetric relativity
Open this publication in new window or tab >>Theoretical and numerical bimetric relativity
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

General relativity (GR) is the standard physical theory describing gravitational interactions. All astrophysical and cosmological observations are compatible with its predictions, provided that unknown matter and energy components are included. These are called dark matter and dark energy.

In addition, GR describes the nonlinear self-interaction of a massless spin-2 field. In particle physics, there are both massless and massive fields having spin 0, 1 and 1/2. It is then well-justified to ask whether a mathematically consistent nonlinear theory describing a massive spin-2 field exists.

The Hassan–Rosen bimetric relativity (BR) is a mathematically consistent theory describing the nonlinear interaction between a massless and a massive spin-2 field. These fields are described by two metrics, out of which only one can be directly coupled to us and determines the geometry we probe.

Since it includes GR, BR is an extension of it and provides us with new astrophysical and cosmological solutions. These solutions, which may give hints about the nature of dark matter and dark energy, need to be tested against observations in order to support or falsify the theory. This requires predictions for realistic physical systems. One such system is the spherically symmetric gravitational collapse of a dust cloud, and its study is the overarching motivation behind the thesis.

Studying realistic physical systems in BR requires the solving of the nonlinear equations of motion of the theory. This can be done in two ways: (i) looking for methods that simplify the equations in order to solve them exactly, and (ii) solving the equations numerically.

The studies reviewed in the thesis provide results for both alternatives. In the first case, the results concern spacetime symmetries (e.g., spherical symmetry) and how they affect particular solutions in BR, especially those describing gravitational collapse. In the second case, inspired by the success of numerical relativity, the results initiate the field of numerical bimetric relativity. The simulations provide us with the first hints about how gravitational collapse works in BR.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2020. p. 187
Keywords
spin-2 fields, extension of general relativity, ghost-free bimetric theory, Hassan–Rosen bimetric relativity, numerical relativity
National Category
Astronomy, Astrophysics and Cosmology Other Physics Topics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-178523 (URN)978-91-7911-004-8 (ISBN)978-91-7911-005-5 (ISBN)
Public defence
2020-03-18, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 8: Manuscript.

Available from: 2020-02-24 Created: 2020-01-31 Last updated: 2020-02-18Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Torsello, FrancescoKocic, MikicaHögås, MarcusMörtsell, Edvard
By organisation
Department of PhysicsThe Oskar Klein Centre for Cosmo Particle Physics (OKC)
In the same journal
Classical and quantum gravity
Other Physics Topics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 58 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf