The paper under review studies the equation \[ \mathcal{P}u:=\left[\Box_{g}+\frac{\xi(\sigma,y)}{\sigma^2}\right]u \] on a domain \(\Omega:= (0, \sigma_{0}) \times I\), where \(\sigma_{0} > 0\) and \(I\) is an open subset of \(\mathbb{R}^{d}\). Here, \(g\) and \(\xi\) denote a Lorentzian metric and a bounded function on \(\Omega\), respectively, while \(\sigma\) and \(y\) are the projections to the \((0, \sigma_{0})\)- and \(I\)-components of \(\Omega\).
The authors find counterexamples to the unique continuation problem, in other words they find solutions to the above equation that are not uniquely determined by their Cauchy data on \(\sigma=0\).