Generalised splitting of spacetime
The 3+1 splitting of space-time used by Arnowitt, Deser and Misner (ADM) is generalized to an \(m+n\) splitting. Thus, the foliating spaces are of arbitrary dimension \(m\) in a space-time of dimension \(m+n\). The shift vector and ADM lapse function are appropriately generalized and a derivation of the generalized Gauss-Codazzi and Gauss-Weingarten equations associated with such a splitting are derived. In addition, the projected components of the Ricci tensor are calculated. Finally, the author considers a globally orthogonal \(m+n\) splitting in which case the above equations assume a more manageable and elegant form. As the author acknowledges, such a study of foliating spaces has previously been done but the value of this paper is in its use of a language more accessible to physicists familiar with the ADM formalism.
scientific article; zbMATH DE number 64318