Spherical gravitational waves and quasi-spherical waves scattered from black string in massive gravity

Hongsheng Zhang,Yang Huang

doi:10.1007/jhep12(2021)056

Abstract

Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution with a special singular reference metric. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear perturbations. We find that the graviton ray can be null in massive gravity by considering full back reaction of the massive gravitational waves to the metric. We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton.

Highlights

JHEP12(2021)056 to Birkhoff’s theorem, spherical wave is strictly forbidden in full theory of GR
We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution with a special singular reference metric
We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton

Summary

Spherical gravitational waves in dRGT massive gravity

Where R denotes the Ricci scalar, Lm labels the Lagrangian of the matter fields, and V (g, f ) is the potential of graviton. V (g, f ) is a function of the physical metric g and reference metric f , which is the critical improvement of dRGT massive gravity. Up to now we have no physical principle to determine the reference metric Sometimes it is taken as a Minkowski one. A black hole solution in massive gravity with singular reference metric is found in [15], and is widely applied in [16,17,18,19,20]. The stability of massive gravity with general singular reference metrics thoroughly explored in [21]. In massive gravity U denotes the Minser-Sharp mass [17], while there is no matter outside the black hole to balance the variation of the mass of the hole. We complete a spherical gravitational wave in massive gravity for vacuum space

Quasi-spherical waves scattered from black strings

Summary