Semianalytical approach for the Vaidya metric in double-null coordinates

We reexamine here a problem considered in detail before by Waugh and Lake: the solution of spherically symmetric Einstein’s equations with a radial flow of unpolarized radiation (the Vaidya metric) in double-null coordinates. This problem is known to be not analytically solvable; the only known explicit solutions correspond to the constant mass case (Schwarzschild solution in Kruskal-Szekeres form) and the linear and exponential mass functions originally discovered by Waugh and Lake. We present here a semianalytical approach that can be used to discuss some qualitative and quantitative aspects of the Vaidya metric in double-null coordinates for generic mass functions. We present also a new analytical solution corresponding to (1/v)-mass function and discuss some physical examples.