Figure 5

Figure 5: $H$ is a dynamical horizon, foliated by marginally trapped surfaces $S$ . $a ^τ$ is the unit time-like normal to $H$ and $^ra$ the unit space-like normal within $H$ to the foliations. Although $H$ is space-like, motions along $^ra$ can be regarded as ‘time evolution with respect to observers at infinity’. In this respect, one can think of $H$ as a hyperboloid in Minkowski space and $S$ as the intersection of the hyperboloid with space-like planes. In the figure, $H$ joins on to a weakly isolated horizon $Δ$ with null normal $a ℓ¯$ at a cross-section $S0$ .