Injectivity Radius of Lorentzian Manifolds

  title={Injectivity Radius of Lorentzian Manifolds},
  author={Binglong Chen and Philippe G. LeFloch},
  journal={Communications in Mathematical Physics},
Motivated by the application to general relativity we study the geometry and regularity of Lorentzian manifolds under natural curvature and volume bounds, and we establish several injectivity radius estimates at a point or on the past null cone of a point. Our estimates are entirely local and geometric, and are formulated via a reference Riemannian metric that we canonically associate with a given observer (p, T) –where p is a point of the manifold and T is a future-oriented time-like unit… 

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