  We use the general solution to the trace of the 4-dimensional Einstein
equations for static, spherically symmetric configurations as a basis for
finding a general class of black hole (BH) metrics, containing one arbitrary
function $g_{tt} = A(r)$ which vanishes at some $r = r_h > 0$, the horizon
radius. Under certain reasonable restrictions, BH metrics are found with or
without matter and, depending on the boundary conditions, can be asymptotically
flat or have any other prescribed large $r$ behaviour. It is shown that this
procedure generically leads to families of solutions unifying non-extremal
globally regular BHs with a Kerr-like global structure, extremal BHs and
symmetric wormholes. Horizons in space-times with zero scalar curvature are
shown to be either simple or double. The same is generically true for horizons
inside a matter distribution, but in special cases there can be horizons of any
order. A few simple examples are discussed. A natural application of the above
results is the brane world concept, in which the trace of the 4D gravity
equations is the only unambiguous equation for the 4D metric, and its solutions
can be continued into the 5D bulk according to the embedding theorems.
