the Bach tensor trivially rescales under the conformal transformation as ${B_{ab} = \Omega^{-2}\,B_{ab}^{{\hbox{\tiny Kundt}}}}$, it remains simple. These calculations are performed in Appendix B.

3.  These explicit components of the Ricci and Bach tensors are substituted into the field equations of Quadratic Gravity, which we already reduced to the expression ${R_{ab}=4k\, B_{ab}}$, see . This immediately leads to a very simple and compact form of these field equations. Moreover, using the Bianchi identities, it can be shown that the whole system reduces just to two equations , for the metric functions $\Omega(r)$ and $\H(r)$, see Appendix C.

By this procedure, we thus arrive at a remarkably simple form of the field equations (\[fieldeqsEWmod\]) for spherically symmetric vacuum spacetimes in Einstein–Weyl gravity and general Quadratic Gravity with ${R=0}$, namely *two ordinary differential equations* for the *two metric functions* $\Omega(r)$ and ${\cal H}(r)$: $$\begin{aligned}
\Omega\Omega''-2{\Omega'}^2 = &\ \tfrac{1}{3}k\, \B_1 \H^{-1} \,, \label{Eq1}\\
\Omega\Omega'{\cal H}'+3\Omega'^2{\cal H}+\Omega^2
 = &\ \tfrac{1}{3}k \,\B_2  \,. \label{Eq2}\end{aligned}$$ The functions $\B_1(r)$ and $\B_2(r)$ denote *two independent components of the Bach tensor*, && \_1 ””, \[B1\]\
&& \_2 ’[H]{}”’-\^2 +2. \[B2\]

Recall also the relation (\[R=0\]), that is ${R=0}$, which is a trace of the field equations . This relation 