20241114 Lucas Dahinden

Morse spacetimes are Lorentz spacetimes with singularities where time behaves like a Morse function. The intention of the definition is that the spacetimes are "nice" but still allow the topology of "space" to change with time. Borde and Sorkin conjectured that such Morse spacetimes are causally continuous (a.k.a. nice) if and only if neither the index nor the coindex of any critical point is 1. This has been recently confirmed by García-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. Thus, the Borde-Sorkin conjecture does not hold. The proof features a low regularity causal structure and causal bubbling.