Does a Nambu-Goto wall emit gravitational waves? Cylindrical Nambu-Goto wall as an example of gravitating nonspherical walls

The gravitational field of a cylindrical Nambu-Goto wall in vacuum spacetime is considered in order to clarify the interaction between Nambu-Goto membranes and gravitational waves. If one neglects the emission of gravitational waves by the wall motion, the spacetime becomes singular. It is also shown that the emission of gravitational waves does occur by the motion of the cylindrical wall if the initial data are singularity free. The energy loss rate due to the radiation of the gravitational waves agrees with that estimated from the test wall motion and the quadrupole formula for the gravitational wave emission. This is quite different from the oscillatory behavior of gravitating Nambu-Goto membranes: the presence of gravity induces the wall to lose its dynamical degree of freedom.