Scattering rigidity for standard stationary manifolds via timelike geodesics

Abstract

We study the scattering rigidity problem for standard stationary manifolds using timelike geodesics with a fixed momentum. Taking advantage of the symmetry of this manifolds, we use Hamiltonian reduction to show that this problem is related to scattering rigidity for $\mathcal{M}\mathcal{P}$-systems, a problem studied before. This gives several new rigidity results (up to some gauge) for this kind of Lorentzian manifolds.

26 pages; typos corrected, more explicit result and hypothesis, references added

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