List of Figures

View Image Figure 1:
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.
View Image Figure 2:
The null parallelogram. After computing the field at point N, the algorithm marches the computation to ℐ+ by shifting the corners by N → n, E → e, S → E, W → N.
View Image Figure 3:
Trousers shaped event horizon obtained by the conformal model.
View Image Figure 4:
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.
View Image Figure 5:
The physical setup for the scattering problem. A star of mass M has undergone spherically symmetric collapse to form a black hole. The ingoing null worldtube 𝒩 lies outside the collapsing matter. Inside 𝒩 (but outside the matter) there is a vacuum Schwarzschild metric. Outside of 𝒩, data for an ingoing pulse is specified on the initial outgoing null hypersurface − 𝒥. As the pulse propagates to the black hole event horizon + ℋ, part of its energy is scattered to + ℐ.
View Image Figure 6:
Black hole excision by matching. A Cauchy evolution, with data at t0 is matched across worldtubes R0 and R1 to an ingoing null evolution, with data at v0, and an outgoing null evolution, with data at u 0. The ingoing null evolution extends to an inner trapped boundary Q, and the outgoing null evolution extends to + ℐ.
View Image Figure 7:
Sequence of slices of the metric component γxy, 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.
View Image Figure 8:
CCM for binary black holes, portrayed in a co-rotating frame. The Cauchy evolution is matched across two inner worldtubes Γ 1 and Γ 2 to two ingoing null evolutions whose inner boundaries excise the individual black holes. The outer Cauchy boundary is matched across the worldtube Γ to an outgoing null evolution extending to ℐ+.