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Curvature Diffusions in General Relativity

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Abstract

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.

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Authors and Affiliations

  1. IRMA, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Jacques Franchi

  2. Université Paris Sud 11, Mathématiques, Bâtiment 425, 91405, Orsay, France

    Yves Le Jan

Authors
  1. Jacques Franchi
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  2. Yves Le Jan
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Correspondence to Jacques Franchi.

Additional information

Communicated by S. Smirnov

Bénéficiaire d’une aide de l’Agence Nationale de la Recherche, no ANR-09-BLAN-0364-01.

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Franchi, J., Jan, Y.L. Curvature Diffusions in General Relativity. Commun. Math. Phys. 307, 351–382 (2011). https://doi.org/10.1007/s00220-011-1312-z

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  • DOI: https://doi.org/10.1007/s00220-011-1312-z

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