Spacetimes with waves

5.8 Spacetimes with waves

[171 ] presents a method to produce initial data configurations containing waves. Given a fixed background metric, it shows how to superimpose a given gravitational wave content. The equations are solved numerically using a multidomain spectral code based on [172

, 168

]. Space is covered by various sphere-like shells and is described up to infinity. When no black hole is present, the origin is covered by a square domain because regularity conditions at the origin, in spherical coordinates, are not handled by [172 , 168 ]. Such a setting is used to generate spacetimes containing i) pure quadrupolar waves ii) flat space with an ingoing pulse and iii) a single black hole superimposed with an ingoing quadrupolar wave.