  A general form of a metric preserving all symmetries of a spherically
symmetric gravitational field and angular momentum in spherical coordinates is
obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely
defines $g_{00}(r)$. Geodesic motion under such metric exactly reproduces the
precession of a planetary orbit, periastron advance of a binary, deflection of
light and {Shapiro time delay} if the determinant of the time-radial parts of
the metric is $-1$. In this model, the total time for a radial round trip of
light is as in the Schwarzschild model, but it allows for light rays to have
different speeds propagating toward or from the massive object. The value of
$g_{01}(r) $ could be obtained by measuring these speeds. All of these metrics
do satisfy Einstein's field equations
