Annales Henri Poincaré

, Volume 12, Issue 5, pp 965–985 | Cite as

Areas and Volumes for Null Cones

  • James D. E. GrantEmail author


Motivated by recent work of Choquet-Bruhat et al. (Class Quantum Gravity 26(135011), 22, 2009), we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop–Gromov relative volume monotonicity theorem and Günther’s volume comparison theorem. We briefly discuss how these estimates may be used to control the null second fundamental form of slices of the null cone in Ricci-flat Lorentzian four-manifolds with null curvature bounded above.


Minkowski Space Ricci Curvature Ricci Tensor Comparison Theorem Null Geodesic 
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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institut für Grundlagen der BauingenieurwissenschaftenLeopold-Franzens-Universität InnsbruckInnsbruckAustria
  2. 2.Fakultät für MathematikUniversität WienWienAustria

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