Vaidya's Radiating Schwarzschild Metric
1965; American Institute of Physics; Volume: 137; Issue: 5B Linguagem: Inglês
10.1103/physrev.137.b1364
ISSN1536-6065
AutoresRichard W. Lindquist, Robert A. Schwartz, Charles W. Misner,
Tópico(s)Relativity and Gravitational Theory
ResumoIn Vaidya's metric for a radiating sphere, $d{s}^{2}=\ensuremath{-}(1\ensuremath{-}2m{r}^{\ensuremath{-}1})d{u}^{2}\ensuremath{-}2dudr+{r}^{2}d{\ensuremath{\Omega}}^{2},$ where $m(u)$ is a nonincreasing function of the retarded time $u=t\ensuremath{-}r$, we verify that $\ensuremath{-}\frac{\mathrm{dm}}{\mathrm{du}}$ 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 $r=2m(\ensuremath{\infty})$ at $u=\ensuremath{\infty}$ (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" $\ensuremath{-}\frac{\mathrm{GL}}{{c}^{3}r}$ associated with a changing mass in the Newtonian $\ensuremath{-}\frac{\mathrm{Gm}}{{r}^{2}}$ field.
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