Regularizing tunnelling calculations of Hawking temperature

Attempts to understand Hawking radiation as tunnelling across a black hole horizon require the consideration of singular integrals. Although Schwarzschild coordinates lead to the standard Hawking temperature, isotropic radial coordinates may appear to produce an incorrect value. It is demonstrated here how the proper regularization of singular integrals leads to the standard temperature for the isotropic radial coordinates as well as for other smooth transformations of the radial variable, which of course describe the same black hole.