  Guided by a Hamiltonian treatment of spherically symmetric geometry, we find
a remarkably simple -- stationary, but not static -- form for the line element
of Schwarzschild (and Reissner-Nordstrom) geometry. The line element continues
smoothly through the horizon; by exploiting this feature we are able to give a
very simple and physically transparent derivation of the Hawking radiance. We
construct the complete Penrose diagram by enforcing time-reversal symmetry.
Finally we outline how an improved treatment of the radiance, including effects
of self-gravitation, can be obtained.

General Relativity and Quantum Cosmology;High Energy Physics - Theory