Scattering rigidity for standard stationary manifolds via timelike geodesics

TL;DR

This paper investigates the scattering rigidity of standard stationary Lorentzian manifolds using timelike geodesics, employing Hamiltonian reduction to connect it with known problems and establish new rigidity results.

Contribution

It introduces a novel approach linking scattering rigidity in stationary manifolds to $ ext{MP}$-systems via Hamiltonian reduction, leading to new rigidity results.

Findings

Established new rigidity results for Lorentzian manifolds.

Connected scattering rigidity to $ ext{MP}$-systems through Hamiltonian reduction.

Provided insights into gauge equivalence in the context of these manifolds.

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 $\mathcal{MP}$-systems, a problem studied before. This gives several new rigidity results (up to some gauge) for this kind of Lorentzian manifolds.