Vaidya's Radiating Schwarzschild Metric

In Vaidya's metric for a radiating sphere, ds^2=- (1-2mr^-1) du^2-2dudr+r^2d^2, where m (u) is a nonincreasing function of the retarded time u=t-r, we verify that -dmdu is the total power output as given by the Landau-Lifshitz stress-energy pseudotensor, and relate it through red-shift and Doppler-shift factors to the apparent luminosity L for an observer moving radially in this gravitational field. We argue that the hypersurface r=2m (u) cannot be realized physically, but see that a hypersurface r=2m () at u= (which is not adequately represented in presently available coordinate systems) shows the total red-shift characteristic of the Schwarzschild "singularity. " The geodesic equations are written out to display a gravitational "induction field" -GL{c^3r} associated with a changing mass in the Newtonian -Gm{r^2} field.