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Can new physics challenge “ old ” computational barriers ?

We discuss the impact of very recent developments of spacetime theory, black hole physics, and cosmology to well established foundational issues of computability theory and logic. Namely, we describe a physical device in relativistic spacetime which can compute a non-Turing computable task, e.g. which can decide the halting problem of Turing machines or whether ZF set theory is consistent or not. Connections with foundation of mathematics and foundation of spacetime theory will be