A. Ishibashi et H. Ishihara, BUBBLE WALL PERTURBATIONS COUPLED WITH GRAVITATIONAL-WAVES, Physical review. D. Particles and fields, 56(6), 1997, pp. 3446-3458
We study a coupled system of gravitational waves and a domain wall whi
ch is the boundary of a vacuum bubble in de Sitter spacetime. To treat
the system, we use the metric junction formalism of Israel. We show t
hat the dynamical degree of the bubble wall is lost and the bubble wal
l can oscillate only while the gravitational waves go across it. This
means that the gravitational back reaction on the motion of the bubble
wall cannot be ignored.