Does a domain wall emit gravitational waves? -- General-relativistic perturbative treatment

The behavior of gravitational wave perturbations on a locally Minkowskian spacetime background containing a planar domain wall is investigated in the gauge-invariant general relativistic framework. It is shown that for this particular background the domain wall does not emit gravitational waves spontaneously by its free oscillation in the first order, although it scatters incidental gravitational waves.