Finsler gravitational waves of (α, β)-type and their observational signature

Abstract

We introduce a new class of (α,β)-type exact solutions in Finsler gravity closely related to the well-known pp-waves in general relativity. Our class contains most of the exact solutions currently known in the literature as special cases. The linearized versions of these solutions may be interpretted as Finslerian gravitational waves, and we investigate the physical effect of such waves. More precisely, we compute the Finslerian correction to the radar distance along an interferometer arm at the moment a Finslerian gravitational wave passes a detector. We come to the remarkable conclusion that the effect of a Finslerian gravitational wave on an interferometer is indistinguishable from that of standard gravitational wave in general relativity. Along the way we also physically motivate a
modification of the Randers metric and prove that it has some very interesting properties.

A Cosmological unicorn solution to Finsler gravity

“…Alternatively, one might interpret this as saying that light can only be received, not emitted. This would mean that we could not describe radar signals or use radar methods [23,[42][43][44], which we certainly can in the physical world. If, on the other hand, y 0 is a spacelike coordinate, the situation becomes even worse, as this would mean that light cannot propagate in the spatial y 0 direction (in contrast to the −y 0 direction).…”

“…To obtain a viable light cone structure, which allows for emission and reception of light rays in all spatial directions at each x ∈ M, we consider a modified unicorn metric, inspired by the construction of modified Randers metrics in [23].…”

“…Our solutions extend the very short list of known exact solutions in Finsler gravity. Indeed, to the best of our knowledge, the only ones currently known in the literature are the (m-Kropina type) Finsler pp-waves [20] and their generalization as very general relativity spacetimes [21], the Randers pp-waves [22], and the pp-waves of general ðα; βÞ-metric type [23].…”

Anisotropic conformal change of conic pseudo-Finsler surfaces, I*

“…Also, the Finslerian Schwarzschild black hole is a warped product of space-time with constant Finslerian curvature in its two-dimensional subspace [19]. For more applications on conic pseudo-Finsler surfaces, see [5,12,18,21].…”