Generalized Damour-Navier-Stokes equation applied to trapping horizons

Eric Gourgoulhon
Phys. Rev. D 72, 104007 – Published 11 November 2005

Abstract

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 31 July 2005

DOI:https://doi.org/10.1103/PhysRevD.72.104007

©2005 American Physical Society

Authors & Affiliations

Eric Gourgoulhon*

  • Laboratoire de l’Univers et de ses Théories, UMR 8102 du C.N.R.S., Observatoire de Paris, F-92195 Meudon Cedex, France

  • *Electronic address: eric.gourgoulhon@obspm.fr

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 72, Iss. 10 — 15 November 2005

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×