Black Holes in Higher Derivative Gravity

It is well known that Einstein Theory of General Relativity has pathological solutions, called black holes, where the theory fails at some point and gives us infinite values.
In order to solve this problems, there exists UV extensions of General Relativity. These kind of theories try to solve the singularity problem, and some of them are actually singularity-free.

Let’s consider the fourth order gravity, with lagrangian density $R + a R^2 – b R_{munu}R^{munu}$. The field equations in this theory become (in vacuum):
begin{align}
nonumber
& R_{munu}- dfrac{1}{2}g_{munu}R+a left( 2RR_{munu} – dfrac{1}{2}g_{munu}R^2
–
2nabla_mu nabla_nu R
+
2g_{munu} square R right)
& – bleft(
– dfrac{1}{2}g_{munu}R_{alphabeta}R^{alphabeta} – nabla_mu nabla_nu R
+
Box R_{munu}
+
dfrac{1}{2} g_{munu} square R
-2 R_{alphamunubeta}R^{alphabeta}
right) = 0
end{align}
How can we find black hole solutions in this theory? If there are no black hole solutions, can we find at least horizon-like solutions? Since this theory in the limit becomes Einstein GR, we could be able to see how black holes appear from this theory in the limit where we recover GR.
Are there any values $a$ and $b$ such that if we have an Einstein GR solution, this solution is also a solution of the higher derivative field equation above?