A specific region of spacetime can be completely invisible to outside observers, no matter how much data they collect from its boundaries.
April 23, 2026
Original Paper
Counterexamples to the Lorentzian Calderón problem
arXiv · 2604.20320
The Takeaway
Standard geometry models long assumed that you could figure out the internal structure of a space by measuring signals at its edges. This proof demonstrates that two entirely different internal structures can produce identical measurements on the outside. This means the interior of certain gravitational regions is fundamentally unknowable through boundary observations alone. It challenges the inverse problem logic used in everything from medical imaging to general relativity. Some parts of our universe might be permanently shielded from our understanding by their own geometry.
From the abstract
We show that two non-isometric, smooth, globally hyperbolic Lorentzian metrics can have the same hyperbolic Dirichlet-to-Neumann map on an infinite cylinder with timelike boundary.