Non-trivial static, spherically symmetric vacuum solution in a non-conservative theory of gravity

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