Abstract
We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This means a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-waves dynamics, using an integral representation originally due to Poisson. Inspired in this progress we tackle the subtle problem on how matter couples to bigravity and concretely if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported in one case by a massless free scalar field and by a wavefront-homogeneous Maxwell field in another. Considering the most general allowed Maxwell source instead is a highly nontrivial task, that we accomplish by exploiting again the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this allow us to find at the end the most general configurations for any matter source.
Highlights
Gravitational theories are characterized by the existence of wavy configurations, as in any other relativistic field theory; they are responsible for propagating the interaction and transferring energy across spacetime, which eventually can be measured independently of where they were generated
One advantage of looking for sumseparable solutions is that it allows to implement the whole residual symmetry [Eq (12) or (23)] to get rid of the nonphysical terms. This clearly exhibits a mode coming from General Relativity as well as two additional physical massive modes that are characteristic of these kind of theories; these are the prevailing modes respecting the symmetries of the system
Euler-Darboux equation, but it is connected to the extension (C14) of Euler-Darboux operators containing the original massless version and whose behavior can be determined again in terms of the standard Euler-Darboux description
Summary
Gravitational theories are characterized by the existence of wavy configurations, as in any other relativistic field theory; they are responsible for propagating the interaction and transferring energy across spacetime, which eventually can be measured independently of where they were generated. Hassan and Rosen [11] showed that the reference metric can be promoted to an independent dynamical one without spoiling the nice features of the original theory (i.e., it is generally covariant and ghost-free), which is the why the resulting theory is called bigravity This is the framework we will work with, so will devote the following section to reviewing its main ingredients. VI by regarding the Siklos operator as a complexified version of Euler-Darboux operators [25,26], which allows us to find the most general AdS waves rigged by the dynamics of bigravity Another controversial issue of bigravity is the way to couple matter, and Sec. VII is devoted to this issue with a discussion on the effective metric and explicit calculations for both scalar and Maxwell fields. Other appendices are devoted to detailed derivations which are essential to obtain the main results of the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
