  We determine the complete space-time metric from the bootstrapped Newtonian
potential generated by a static spherically symmetric source in the surrounding
vacuum. This metric contains post-Newtonian parameters which can be further
used to constrain the complete underlying dynamical theory. For values of the
post-Newtonian parameters within experimental bounds, the reconstructed metric
appears very close to the Schwarzschild solution of General Relativity in the
whole region outside the event horizon. The latter is however larger in size
for the same value of the mass compared to the Schwarzschild case.
