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The Bakry-Émery Ricci Tensor: Application to Mass Distribution in Space-time

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Abstract

The Bakry-Émery Ricci tensor gives an analogue of the Ricci tensor for a Riemannian manifold with a smooth function. This notion motivates a new version of Einstein’s field equation in which the mass becomes part of geometry. This new field equation is purely geometric and is obtained from an action principle which is formed naturally by the scalar curvature associated with the Bakry-Émery Ricci tensor.

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Authors and Affiliations

  1. Department of pure mathematics,Faculty of science, Imam Khomeini International University, Norouzian Avenue, Qazvin, Iran

    Ghodratallah Fasihi-Ramandi

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  1. Ghodratallah Fasihi-Ramandi
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Correspondence to Ghodratallah Fasihi-Ramandi.

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Fasihi-Ramandi, G. The Bakry-Émery Ricci Tensor: Application to Mass Distribution in Space-time. Gravit. Cosmol. 27, 42–46 (2021). https://doi.org/10.1134/S0202289321010096

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  • DOI: https://doi.org/10.1134/S0202289321010096

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