The advanced/ingoing Vaidya solution Eq(7) is especially useful in black-hole physics as it is one of the few existing exact dynamical solutions. For example, it is often employed to investigate the differences between different definitions of the dynamical black-hole boundaries, such as the classical event horizon and the quasilocal trapping horizon; and as shown by Eq(17), the evolutionary hypersurface r = 2 M ( v ) is always a marginally outer trapped horizon ( θ θ ( ℓ ℓ ) = 0 , θ θ ( n ) < 0 ).