  Following [Fra08, AF14] we construct Rabinowitz Floer homology for negative
line bundles over symplectic manifolds and prove a vanishing result.
  In [Rit14] Ritter showed that symplectic homology of these spaces does not
vanish, in general. Thus, the theorem
$\mathrm{SH}=0\Leftrightarrow\mathrm{RFH}=0$, [Rit13], does not extend beyond
the symplectically aspherical situation. We give a conjectural explanation in
terms of the Cieliebak-Frauenfelder-Oancea long exact sequence [CFO10].
