Hawking temperatures for the Vaidya and the Reissner-Nordstrom-Vaidya black holes

We derive the Hawking temperature for both the Vaidya and the Reissner-Nordstrom-Vaidya black holes in two methods, the radial null geodesic method and the complex path method. Both black holes differ in some ways including the charge content and the number of horizons: the Vaidya black hole is charge-less and it has a single horizon while the Reissner-Nordstrom-Vaidya black hole is charged and it has two horizons. We obtain that the Hawking temperature for both black holes depends on their masses and on the radial change of their masses. Black hole with greater mass has a lesser Hawking temperature. We also obtain that there is a condition that should be fulfilled in order to guaranty positive values of the Hawking temperature. Some special cases for the Reissner-Nordstrom-Vaidya black hole are also discussed.