Abstract
The possibility of matter coupling to two metrics at once is considered. This appears natural in the most general ghost-free, bimetric theory of gravity, where it unlocks an additional symmetry with respect to the exchange of the metrics. This double coupling, however, raises the problem of identifying the observables of the theory. It is shown that if the two metrics couple minimally to matter, then there is no physical metric to which all matter would universally couple, and that moreover such an effective metric generically does not exist even for an individual matter species. By studying point particle dynamics, a resolution is suggested in the context of Finsler geometry.
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Acknowledgments
We thank John Barrow and Fawad Hassan for useful discussions. This work has benefitted from Y. Akrami’s and A. Solomon’s stays at the University of Oslo and Nordita, as well as at the Structure of Gravity and Space-Time conference in Oxford and from many enlightening discussions therein. Y. Akrami is supported by the European Research Council (ERC) Starting Grant StG2010-257080. A. Solomon acknowledges support from the David Gledhill Research Studentship, Sidney Sussex College, University of Cambridge; and the Isaac Newton Fund and Studentships, University of Cambridge.
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Akrami, Y., Koivisto, T.S. & Solomon, A.R. The nature of spacetime in bigravity: Two metrics or none?. Gen Relativ Gravit 47, 1838 (2015). https://doi.org/10.1007/s10714-014-1838-4
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DOI: https://doi.org/10.1007/s10714-014-1838-4