On Gravitational anomaly and Hawking radiation near weakly isolated horizon

Based on the idea of the work by Wilczek and his collaborators, we consider the gravitational anomaly near weekly isolated horizon. We find that there exists a universal choice of tortoise coordinate for any weakly isolated horizon. Under this coordinate, the leading behavior of a quite arbitrary scalar field near horizon is a 2-dimensional chiral scalar field. This means we can extend the idea of Wilczek and his collaborators to more general cases and show the relation between gravitational anomaly and Hawking radiation is a universal property of black hole horizon.