  We analyse the vacuum static spherically symmetric space-time for a specific
class of non-conservative theories of gravity based on the Rastall's theory. We
obtain a new vacuum solution which has the same structure as the
Schwarzschild-de Sitter solution in the General Relativity theory obtained with
a cosmological constant playing the r\^ole of source. We further discuss the
structure (in particular, the coupling to matter fields) and some cosmological
aspects of the underline non-conservative theory
