I've been studying gravity with a dynamical preferred frame, namely one in which the preferred frame is set by the existence of a unit time-like vector field called the "aether". I've been using this link:
When trying to look for spherically symmetric and static solutions of this theory, the aether can be written as \begin{equation} u = a(r) \partial_t + b(r) \partial_r \end{equation}
(equation (11) of the link). Does anyone know why the vector can be written this way? All the papers I find on similar subjects don't explain why as well...
Thank you!