  Since Schwarzshild discovered the point-mass solution to Einstein's equations
that bears his name, many equivalent forms of the metric have been catalogued.
Using an elementary coordinate transformation, we derive the most general form
for the stationary, spherically-symmetric vacuum metric, which contains one
free function. Different choices for the function correspond to common
expressions for the line element. From the general metric, we obtain particle
and photon trajectories, and use them to specify several time coordinates
adapted to physical situations. The most general form of the metric is only
slightly more complicated than the Schwarzschild form, which argues effectively
for teaching the general line element in place of the diagonal metric.

General Relativity and Quantum Cosmology