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 u0. 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.