SHEAR-FREE NULL QUASI-SPHERICAL SPACE-TIMES

We study the residual gauge freedom within the null quasi-spherical (N QS) gauge for space-times admitting an expanding shear-free null folia tion. By constructing the most general NQS coordinates subordinate to such a foliation, we obtain both a clear picture of the geometric natu re of the residual coordinate freedom, and an explicit construction of nontrivial NQS metrics representing some well-known space-times, such as Schwarzschild, accelerated Minkowski, and Robinson-Trautman. These examples will be useful in testing numerical evolution codes. The geo metric gauge freedom consists of an arbitrary boost and rotation at ea ch coordinate sphere-and this freedom may be used to normalise the coo rdinate to an ''inertial'' frame. (C) 1997 American Institute of Physi cs.