  We study structure of solutions of the recently constructed minimal
extensions of Einstein's gravity in four dimensions at the quartic curvature
level. The extended higher derivative theory, just like Einstein's gravity, has
only a massless spin-two graviton about its unique maximally symmetric vacuum.
The extended theory does not admit the Schwarzschild or Kerr metrics as exact
solutions, hence there is no issue of Schwarzschild type singularity but,
approximately, outside a source, spherically symmetric metric with the correct
Newtonian limit is recovered. We also show that for all Einstein space-times,
square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet
invariant) obeys a non-linear scalar Klein-Gordon equation.
