  In d+1 dimensions we solve the equations of motion for the case of gravity
minimally or conformally coupled to a scalar field. For the minimally coupled
system the equations can either be solved directly or by transforming vacuum
solutions, as shown before in 3+1 dimensions by Buchdahl. In d+1 dimensions the
solutions have been previously found directly by Xanthopoulos and Zannias. Here
we first rederive these earlier results, and then extend Buchdahl's method of
transforming vacuum solutions to d+1 dimensions. We also review the conformal
coupling case, in which d+1 dimensional solutions can be found by extending
Bekenstein's method of conformal transformation of the minimal coupling
solution. Combining the extended versions of Buchdahl transformations and
Bekenstein transformations we can in arbitrary dimensions always generate
solutions of both the minimal and the conformal equations from known vacuum
solutions.
