  The Tolman-Bondi and Vaidya solutions are two solutions to Einstein equations
which describe dust particles and null fluid, respectively. We show that it is
possible to match the two solutions in one single spacetime, the
Tolman-Bondi--Vaidya spacetime. The new spacetime is divided by a null surface
with Tolman-Bondi dust on one side and Vaidya fluid on the other side. The
differentiability of the spacetime is discussed. By constructing a specific
solution, we show that the metric across the null surface can be at least $C^1$
and the stress-energy tensor is continuous.
