  Morse spacetime is a model of singular Lorentzian manifold, built upon a
Morse function which serves as a global time function outside its critical
points. The Borde-Sorkin conjecture states that a Morse spacetime is causally
continuous if and only if the index and coindex of critical points of the
corresponding Morse function are both different from 1. The conjecture has
recently been confirmed by Garcia Heveling for the case of small anisotropy and
Euclidean background metric. Here, we provide a complementary counterexample: a
four dimensional Morse spacetime whose critical point has index 2 and large
enough anisotropy is causally discontinuous and thus the Borde-Sorkin
conjecture does not hold. The proof features a low regularity causal structure
and causal bubbling.
