Abstract
In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields. The theory is the fully diffeomorphism and local Lorentz invariant extension of a previous construction which involved a fixed reference vierbein. Certain vierbein components can be shifted by local Lorentz transformations and do not enter the associated metric tensors. We parameterize these components by an antisymmetric tensor field and give them a kinetic term in the action, thereby promoting them to dynamical variables. In addition, the action contains two Einstein-Hilbert terms and an interaction potential whose form is inspired by ghost-free massive gravity and bimetric theory. The resulting theory describes the interactions of a massless spin-2, a massive spin-2 and an antisymmetric tensor field. It can be generalized to the case of multiple massive spin-2 fields and multiple antisymmetric tensor fields. The absence of additional and potentially pathological degrees of freedom is verified in an ADM analysis. However, the antisymmetric tensor fluctuation around the maximally symmetric background solution has a tachyonic mass pole.
Highlights
In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields
This second metric can be promoted to a dynamical field, resulting in a classically consistent bimetric theory, which describes the nonlinear interactions of a massless and a massive spin-2 field [14]
We demonstrate that the action proposed in Ref. [30] can be generalized to a fully dynamical theory for two interacting vierbein fields eaμ and eaμ
Summary
We demonstrate that the action proposed in Ref. [30] can be generalized to a fully dynamical theory for two interacting vierbein fields eaμ and eaμ. [30] can be generalized to a fully dynamical theory for two interacting vierbein fields eaμ and eaμ. The result is a ghost-free bimetric action in vierbein formulation with dynamical Lorentz components which we parameterize in terms of the antisymmetric components Bμν = eaμηabebν −eaμηabebν. The number of propagating degrees of freedom in this new setup is 2 + 5 + 3, corresponding to a massless spin-2, a massive spin and a massive antisymmetric tensor. This is verified both at the linear and at the fully nonlinear level. Indices are raised and lowered by gμν and the inverse gμν on its curvatures and on objects related to the antisymmetric tensor.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
