Vaidya's Radiating Schwarzschild Metric

In Vaidya's metric for a radiating sphere, ds²=-(1-2mr^-1)du²-2dudr+r²dΩ², where $m(u)$ is a nonincreasing function of the retarded time u=t-r, we verify that -dm/du 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" -GLc³r associated with a changing mass in the Newtonian -Gmr² field.