Bimetric variational principle for general relativity

Abstract

The bimetric variational principle is a subtle reinterpretation of general relativity that assumes the spacetime connection to be generated by an independent metric. Unlike the so called Palatini formalism that promotes the connection into a fundamental field, the new variational principle results in a physically distinct theory since the potential for the connection carries new degrees of freedom. The connection-generating metric naturally allows also an antisymmetric component. This sets torsion propagating! It is also shown here that while in the most straightforward generalization of the Einstein-Hilbert action the nonmetric degrees of freedom become ghosts, there exist very simple actions which give rise to viable theories at the linearised level when subjected to the bimetric variational principle. However, the non linear interactions might bring unpleasant features like the Boulware-Deser ghost. This remains to be explored since this new type of bimetric theories does not, in principle, lie in the class of usual bimetric theories where non-linear interactions inevitably come in with new ghost-like degrees of freedom.