  The tunneling effect near a weakly isolated horizon (WIH) has been studied.
By applying the null geodesic method of Parikh and Wilczek and Hamilton-Jacibi
method of Angheben et al. to a weakly isolated horizon, we recover the
semiclassical emission rate in the tunneling process. We show that the
tunneling effect exists in a wide class of spacetimes admitting weakly isolated
horizons. The general thermodynamic nature of WIH is then confirmed.
