The three applications of characteristic evolution with data given on an initial null hypersurface N and boundary B. The shaded regions indicate the corresponding domains of dependence.
The null parallelogram. After computing the field at point , the algorithm marches the computation to by shifting the corners by , , , .
Trousers shaped event horizon obtained by the conformal model.
Upper left: Tidal distortion of approaching black holes Upper right: Formation of sharp pincers just prior to merger. Middle left: Temporarily toroidal stage just after merger. Middle right: Peanut shaped black hole after the hole in the torus closes. Lower: Approach to final equilibrium.
The physical setup for the scattering problem. A star of mass has undergone spherically symmetric collapse to form a black hole. The ingoing null worldtube lies outside the collapsing matter. Inside (but outside the matter) there is a vacuum Schwarzschild metric. Outside of , data for an ingoing pulse is specified on the initial outgoing null hypersurface . As the pulse propagates to the black hole event horizon , part of its energy is scattered to .
Black hole excision by matching. A Cauchy evolution, with data at is matched across worldtubes and to an ingoing null evolution, with data at , and an outgoing null evolution, with data at . The ingoing null evolution extends to an inner trapped boundary , and the outgoing null evolution extends to .
Sequence of slices of the metric component , evolved with the linear matched Cauchy-characteristic code. In the last snapshot, the wave has propagated cleanly onto the characteristic grid with negligible remnant noise.
CCM for binary black holes, portrayed in a co-rotating frame. The Cauchy evolution is matched across two inner worldtubes and to two ingoing null evolutions whose inner boundaries excise the individual black holes. The outer Cauchy boundary is matched across the worldtube to an outgoing null evolution extending to .
© Max Planck Society and the author(s)