Figure 4

Figure 4: Penrose diagrams of Schwarzschild–Vaidya metrics for which the mass function $M (v )$ vanishes for $v ≤ 0$ [138]. The space-time metric is flat in the past of $v = 0$ (i.e., in the shaded region). In the left panel, as $v$ tends to infinity, $M˙$ vanishes and $M$ tends to a constant value $M0$ . The space-like dynamical horizon $H$ , the null event horizon $E$ , and the time-like surface $r = 2M0$ (represented by the dashed line) all meet tangentially at $+ i$ . In the right panel, for $v ≥ v0$ we have $M˙ = 0$ . Space-time in the future of $v = v0$ is isometric with a portion of the Schwarzschild space-time. The dynamical horizon $H$ and the event horizon $E$ meet tangentially at $v = v 0$ . In both figures, the event horizon originates in the shaded flat region, while the dynamical horizon exists only in the curved region.