A Simple Stationary Line Element for the Schwarzschild Geometry, and Some Applications

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.