2003/12/03 by S. V. Chervon, S. Chervon, F. Dahia +1
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physleta.2004.04.033
published as Phys.Lett. A326 (2004) 171-177 · 17 pages/ RevTex
arxiv created 2003/12/03 · openalex publication_date 2004/04/30 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate harmonic maps in the context of isometric embeddings when the target space is Ricci-flat and has codimension one. With the help of the Campbell-Magaard theorem we show that any n-dimensional (n\geqslant 3) Lorentzian manifold can be isometrically and harmonically embedded in a (n+1)-dimensional semi-Riemannian Ricci-flat space. We then extend our analysis to the case when the target space is an Einstein space. Finally, as an example, we work out the harmonic and isometric embedding of a Friedmann-Robertson-Walker spacetime in a five-dimensional Ricci-flat space and proceed to obtain a general scheme to minimally embed any vacuum solution of general relativity in Ricci-flat spaces with codimension one.