Testing general relativity and exploring possible departures has received further input with the possibility to do so through gravitational waves emitted in strongly gravitating/highly dynamical scenarios and also through the availability of exquisitely sensitive cosmological observations. However, most extensions suffer from severe pathologies at the mathematical level which have stymied a thorough exploration of putative theories. With the aid of a model problem which captures typical pathologies, we explore suggested methods to control them. We find that the approach that modifies the equations to control higher-order gradients is both robust and efficient.
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A 2019 study studied this question.