In general relativity, the Vaidya metric describes the non-empty external spacetime of a spherically symmetric and nonrotating star which is either emitting or absorbing null dusts. It is named after the Indian physicist Prahalad Chunnilal Vaidya and constitutes the simplest non-static generalization of the non-radiative Schwarzschild solution to Einstein's field equation, and therefore is also called the "radiating(shining) Schwarzschild metric".

The Schwarzschild metric as the static and spherically symmetric solution to Einstein's equation reads

To remove the coordinate singularity of this metric at ${\displaystyle r=2M}$, one could switch to the Eddington–Finkelstein coordinates. Thus, introduce the "retarded(/outgoing)" null coordinate ${\displaystyle u}$ by

and Eq(1) could be transformed into the "retarded(/outgoing) Schwarzschild metric"

or, we could instead employ the "advanced(/ingoing)" null coordinate ${\displaystyle v}$ by

so Eq(1) becomes the "advanced(/ingoing) Schwarzschild metric"

Eq(3) and Eq(5), as static and spherically symmetric solutions, are valid for both ordinary celestial objects with finite radii and singular objects such as black holes. It turns out that, it is still physically reasonable if one extends the mass parameter ${\displaystyle M}$ in Eqs(3) and Eq(5) from a constant to functions of the corresponding null coordinate, ${\displaystyle M(u)}$ and ${\displaystyle M(v)}$ respectively, thus

The extended metrics Eq(6) and Eq(7) are respectively the "retarded(/outgoing)" and "advanced(/ingoing)" Vaidya metrics. It is also sometimes useful to recast the Vaidya metrics Eqs(6)(7) into the form