Hawking radiation, effective actions and covariant boundary conditions

From an appropriate expression for the effective action, the Hawking radiation from charged black holes is derived, using only covariant boundary conditions at the event horizon. The connection of our approach with the Unruh vacuum and the recent analysis [S.P. Robinson, F. Wilczek, Phys. Rev. Lett. 95 (2005) 011303, gr-qc/0502074; S. Iso, H. Umetsu, F. Wilczek, Phys. Rev. Lett. 96 (2006) 151302, hep-th/0602146; R. Banerjee, S. Kulkarni, arXiv: 0707.2449 [hep-th]] of Hawking radiation using anomalies is established.