English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we give a complete classification of vacuum branes, i.e.,everywhere umbilical time-like hypersurfaces whose extrinsic curvature is aconstant multiple of the induced metric, K_mn=k g_mn, in D-dimensional staticspacetimes with spatial symmetry G(D-2,K), where G(n,K) is the isometry groupof an n-dimensional space with constant sectional curvature K. D>=4 is assumed.It is shown that all possible configurations of a brane are invariant under anisometry subgroup G(D-3,K') for some K'>= K. In particular, configurations of abrane with non-zero k are always G(D-2,K) invariant, except for those in fivespecial one-parameter families of spacetimes. Further, such G(D-2,K)-invariantconfigurations are allowed only in spacetimes whose Ricci tensors are isotropicin the two planes orthogonal to each G(D-2,K)-orbit, or for special values ofk, which do not exist in generic cases. On the basis of these results, we provethe non-existence of a vacuum brane with black hole geometry in static bulkspacetimes with spatial symmetry G(D-2,K). We also discuss mathematicalimplications of these results.Comment: 42 pages in LaTeX with the PTP style. No figure. Minor errors are  corrected, and notations are partially change

Vacuum Branes in D-Dimensional Static Spacetimes with Spatial Symmetry IO(D - 2), O(D - 1) or O+(D - 2,1)