The Brans-Dicke-Rastall theory

Understand

We formulate a theory combining the principles of a scalar-tensor gravity and Rastall's proposal of a violation of the usual conservation laws.

• We obtain a scalar-tensor theory with two parameters $\omega$ and $\lambda$, the latter quantifying the violation of the usual conservation laws.
• The only exact spherically symmetric solution is that of Robinson-Bertotti besides Schwarzschild solution.
• A PPN analysis reveals that General Relativity results are reproduced when $\lambda = 0$.