  We analyze an alternative theory of gravity characterized by metrics that are
tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is
supposed to hold. The simplest expression for the action of gravitational field
is used.Taking the metric and trace of connections as dynamical variables,the
field equations in the absence of matter and other kinds of sources are
derived.The solutions of these equations are obtained for the case of vacuum
static spherical symmetric spacetime.The null geodesics and advance of
perihelion of ellipes are discussed.We confirm a subclass of solutions is
regular for r>0 and there is no event horizon while it is singular at r=0.
