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Isometric embeddings in cosmology and astrophysics

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Abstract

Recent interest in higher-dimensional cosmological models has prompted some significant work on the mathematical technicalities of how one goes about embedding spacetimes into some higher-dimensional space. We survey results in the literature (existence theorems and simple explicit embeddings); briefly outline our work on global embeddings as well as explicit results for more complex geometries; and provide some examples. These results are contextualized physically, so as to provide a foundation for a detailed commentary on several key issues in the field such as: the meaning of ‘Ricci equivalent’ embeddings; the uniqueness of local (or global) embeddings; symmetry inheritance properties; and astrophysical constraints.

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Authors and Affiliations

  1. Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa

    GARETH AMERY, JOTHI MOODLEY & JAMES PAUL LONDAL

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  1. GARETH AMERY
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  2. JOTHI MOODLEY
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  3. JAMES PAUL LONDAL
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Correspondence to GARETH AMERY.

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AMERY, G., MOODLEY, J. & LONDAL, J.P. Isometric embeddings in cosmology and astrophysics. Pramana - J Phys 77, 415–428 (2011). https://doi.org/10.1007/s12043-011-0161-9

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