2005/08/31 by Eric Gourgoulhon, Éric Gourgoulhon · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #astro-ph #gr-qc
paper · pdf · doi:10.1103/physrevd.72.104007
published as Phys.Rev. D72 (2005) 104007 · Added subsection IV.D; corrected an error in Appendix A; added some references; accepted for publication in Phys. Rev. D (16 pages, 4 EPS figures)
arxiv created 2005/10/19 · openalex publication_date 2005/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
An identity is derived from the Einstein equation for any hypersurface H which can be foliated by spacelike two-dimensional surfaces. In the case where the hypersurface is null, this identity coincides with the two-dimensional Navier-Stokes-like equation obtained by Damour in the membrane approach to a black hole event horizon. In the case where H is spacelike or null and the 2-surfaces are marginally trapped, this identity applies to Hayward's trapping horizons and to the related dynamical horizons recently introduced by Ashtekar and Krishnan. The identity involves a normal fundamental form (normal connection 1-form) of the 2-surface, which can be viewed as a generalization to non-null hypersurfaces of the Hajicek 1-form used by Damour. This 1-form is also used to define the angular momentum of the horizon. The generalized Damour-Navier-Stokes equation leads then to a simple evolution equation for the angular momentum.