Exact ghost-free bigravitational waves
arXiv:1801.06764 · doi:10.1103/PhysRevD.97.084045
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.
arXiv comment25 pages
References in corpus (29)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
- GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
- GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
- Resummation of Massive Gravity
- GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
- Massive Gravity in Three Dimensions
- Bimetric Gravity from Ghost-free Massive Gravity
- On couplings to matter in massive (bi-)gravity
- Bending AdS Waves with New Massive Gravity
- Exploring AdS Waves Via Nonminimal Coupling
- Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe
- Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of non-twisting type N solutions
- pp Waves of Conformal Gravity with Self-Interacting Source
- Zwei-Dreibein Gravity
- Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of non-twisting type N solutions
- Gravitational Wave Oscillations in Bigravity
- Mass eigenstates in bimetric theory with matter coupling
- Consistent massive graviton on arbitrary backgrounds
- Gordon and Kerr-Schild ansatze in massive and bimetric gravity
- Decoherence of Gravitational Wave Oscillations in Bigravity
- Rotating (A)dS black holes in bigravity
- Gravitational Waves in Ghost Free Bimetric Gravity
- Role of symmetries in the Kerr-Schild derivation of the Kerr black hole
- Logarithmic AdS Waves and Zwei-Dreibein Gravity
- Scalar Fields Nonminimally Coupled to pp Waves
- Higher-dimensional AdS waves and pp-waves with conformally related sources
- On the Residual Symmetries of the Gravitational Field