4 papers
math.DG2026
On the causality of gravitational pp-wave spacetimes: A null version of Anderson's rigidity theorem
Hannah Cairo
We prove that plane waves are the only gravitational pp-wave spacetimes which are distinguishing; in particular, they are the only strongly causal ones. This is used to prove a nul…
gr-qc2026
On the completeness of gravitational pp-wave spacetimes: A counterexample to the {Ehlers--Kundt} conjecture
Hannah Cairo
This paper concerns the geometry of gravitational pp-wave spacetimes. We give a counterexample to the Ehlers--Kundt conjecture. In fact, we show that geodesic completeness is gener…
math.CA2025
Power loss for the Mizohata-Takeuchi conjecture on convex hypersurfaces
Hannah Cairo, Ruixiang Zhang
We find a family of compact hypersurfaces where the local Mizohata-Takeuchi Conjecture fails with a power loss of for any . Moreover, this family i…
math.CA2025
A Counterexample to the Mizohata-Takeuchi Conjecture
Hannah Cairo
We derive a family of estimates of the X-Ray transform of positive measures in , which we use to construct a -loss counterexample to the Mizohata-Takeuch…