We put Dirac equation of near the event horizons of black hole change into second order equation of by employing the new tortoise coordinate transformation;get the Hawking radiation temperature near event horizons and Hawking radiation spectrum.

The temperatures of Schwarzchild and Kerr-Newman black holes computed by this method are identical with the result computed by the definition of black hole s surface gravity,while the temperature of Vaidya black hole accords with the outcome calculated by reducing the Klein-Gordon equation near the event horizon to standard form with a new tortoise coordinate transformation.

Motivated by the work of Robinson et al,we have researched Hawking radiation from the event horizon of Vaidya black hole via covariant anomalies theory and general tortoise coordinate transformation,and the result shows that the Hawking temperature can be correctly determined by covariant anomalies at the horizon.

In Vaidya-Bonner spacetime,the quantum nonthermal radiation of black hole was researched through studying Hamilton-Jacobi equation by using Lagging Eddington-Finketstein coordinate and tortoise coordinate transformation.

In Vaidya spacetime, the quantum nonthermal radiation of black hole was studied through studying HamiltonJacobi equation by using Lagging Eddington coordinate and tortoise coordinate transformation, which shows the study of the Lagging Eddington coordinate and that of the leading Eddington coordinate have the same result.

The variations in Hamilton-Jacobi equation in curved spacetime are separated by means of tortoise coordinate transform.