Black holes: from event horizons to trapping horizons - LUTH ...

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Viscous fluid analogy Case of future trapping horizons Definition [Hayward, PRD 49, 6467 (1994)] : H is a future trapping horizon iff θ (ℓ) = 0 and θ (k) < 0. The generalized Damour-Navier-Stokes equation reduces then to S Lh Ω (ℓ) + θ (h) Ω (ℓ) = Dκ − D · σ (m) − 1 2 Dθ(h) − θ (k) DC + 8πq ∗ T · m [EG, PRD 72, 104007 (2005)] NB: Notice the change of sign in the − 1 2 Dθ(h) term with respect to the original Damour-Navier-Stokes equation Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 29 / 38
Viscous fluid analogy Case of future trapping horizons Definition [Hayward, PRD 49, 6467 (1994)] : H is a future trapping horizon iff θ (ℓ) = 0 and θ (k) < 0. The generalized Damour-Navier-Stokes equation reduces then to S Lh Ω (ℓ) + θ (h) Ω (ℓ) = Dκ − D · σ (m) − 1 2 Dθ(h) − θ (k) DC + 8πq ∗ T · m [EG, PRD 72, 104007 (2005)] NB: Notice the change of sign in the − 1 2 Dθ(h) term with respect to the original Damour-Navier-Stokes equation The explanation: it is θ (m) which appears in the general equation and event horizon (m = h) : (m) (ℓ) θ = θ θ (m) + θ (h) = 2θ (ℓ) =⇒ trapping horizon (θ (ℓ) = 0) : θ (m) = −θ (h) Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 29 / 38
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Black holes: from event horizons to
Page 3 and 4: Outline Concept of black hole and e
Page 5 and 6: Concept of black hole and event hor
Page 15 and 16: Local approaches to black holes Loc
Page 17 and 18: Local approaches to black holes Wha
Page 27 and 28: Local approaches to black holes Lin
Page 29 and 30: Local approaches to black holes Con
Page 35 and 36: Local approaches to black holes Exa
Page 37 and 38: Local approaches to black holes Fol
Page 39 and 40: Local approaches to black holes Fol
Page 41 and 42: Local approaches to black holes Evo
Page 43 and 44: Outline Viscous fluid analogy 1 Con
Page 45 and 46: Viscous fluid analogy Concept of bl
Page 47 and 48: Viscous fluid analogy Original Damo
Page 49 and 50: Viscous fluid analogy Original Damo
Page 51 and 52: Viscous fluid analogy Generalizatio
Page 53: Viscous fluid analogy Null limit (e
Page 57 and 58: Viscous fluid form Viscous fluid an
Page 59 and 60: Angular momentum and area evolution
Page 69 and 70: Outline Applications to numerical r
Page 71: Review articles References A. Ashte
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