  This brief note wants to bring to attention that the formulation of
physically reasonable initial-boundary value problems for wave equations in
Lorentzian space-times is not unique, i.e., that there are inequivalent such
formulations that lead to a different outcome of the stability discussion of
the solutions. For demonstration, the paper uses the case of the wave equation
on the right Rindler wedge in 2-dimensional Minkowski space. The used methods
can be generalized to wave equations on stationary globally hyperbolic
space-times with horizons in higher dimensions, such as Schwarzschild and Kerr
space-times.
