Equation of motion for a domain wall coupled to the gravitational field

The equation of motion for a domain wall coupled to the gravitational field is derived from the Nambu-Goto action. The domain wall is treated as a source of the gravitational field and the gravitational back reaction on the wall motion is taken into account. The perturbed equation is also obtained, and is expressed in terms of the gauge-invariant variables in a general spherically symmetric background case.