The covariant approach to static spacetimes in Einstein and extended gravity theories

Abstract We present a covariant study of static space-times, as such and solutions gravity theories. By expressing the relevant tensors through velocity acceleration vectors that characterise field equations provide natural non-redundant set scalar equations. The same suggest form Faraday tensor, is studied in itself (non)-linear electrodynamics. In spherical symmetry, we evaluate explicit expressions Ricci, Weyl, Cotton Bach tensors. Simple restrictions on coefficients yield well known new Einstein, f ( R ), Conformal gravity, with or without charges, vacuo fluid source.