Generalized Damour-Navier-Stokes equation applied to trapping horizons
- Laboratoire de l'Univers et de ses Theories, UMR 8102 du C.N.R.S., Observatoire de Paris, F-92195 Meudon Cedex (France)
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.
- OSTI ID:
- 20711560
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 72, Issue 10; Other Information: DOI: 10.1103/PhysRevD.72.104007; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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