A Simple Stationary Line Element for the Schwarzschild Geometry, and Some Applications
Per Kraus, Frank Wilczek
Abstract
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.
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