Boundary conditions and Maxwell’s equations

The article on black hole mergers by Thomas Baumgarte and Stuart Shapiro (PHYSICS TODAY, October 2011, page 32) was extremely well written and informative. I especially appreciated the use of Maxwell’s equations as a mechanism for explaining the concepts, and I much enjoyed carrying out the exercise suggested in box 2. However, it occurred to me that something is missing in connection with the final result as given in equation 2c. Although it is clearly a wave equation and therefore any constraint violations may indeed “propagate away,” as the authors suggest, it is also clear that the equation will accept a constant solution or even an exponentially growing one. What remains unclear is why the “propagate away” option is the one that should take precedence in actual calculations.