  Gravitational wave emission is considered to be the driving force for the
evolution of short-period cataclysmic binary stars, making them a potential
test for the validity of General Relativity. In spite of continuous refinements
of the physical description, a 10% mismatch exists between the theoretical
minimum period ($P_{\rm turn} \simeq 70$ min) and the short-period cut-off
($P_{\rm min} \simeq 80$ min) observed in the period distribution for
cataclysmic variable binaries. A possible explanation for this mismatch was
associated with the use of the Roche model. We here present a systematic
comparison between self-consistent, numerically constructed sequences of
hydrostatic models of binary stars and Roche models of semi-detached binaries.
On the basis of our approach, we also derive a value for the minimum period of
cataclysmic variable binaries. The results obtained through the comparison
indicate that the Roche model is indeed very good, with deviations from the
numerical solution which are of a few percent at most. Our results therefore
suggest that additional sources of angular momentum loss or alternative
explanations need to be considered in order to justify the mismatch.
