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

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Local approaches to black holes What is a trapped surface ? 2/ The definition S : closed (i.e. compact without boundary) spacelike 2-dimensional surface embedded in spacetime (M , g) Being spacelike, S lies outside the light cone ∃ two future-directed null directions orthogonal to S: ℓ = outgoing, expansion θ (ℓ) k = ingoing, expansion θ (k) In flat space, θ (k) < 0 and θ (ℓ) > 0 Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 11 / 38
Local approaches to black holes What is a trapped surface ? 2/ The definition S : closed (i.e. compact without boundary) spacelike 2-dimensional surface embedded in spacetime (M , g) Being spacelike, S lies outside the light cone ∃ two future-directed null directions orthogonal to S: ℓ = outgoing, expansion θ (ℓ) k = ingoing, expansion θ (k) In flat space, θ (k) < 0 and θ (ℓ) > 0 S is trapped ⇐⇒ θ (k) < 0 and θ (ℓ) < 0 [Penrose 1965] S is marginally trapped ⇐⇒ θ (k) < 0 and θ (ℓ) = 0 Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 11 / 38
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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
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Page 29 and 30: Local approaches to black holes Con
Page 35 and 36: Local approaches to black holes Exa
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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 and 54: Viscous fluid analogy Null limit (e
Page 55 and 56: Viscous fluid analogy Case of futur
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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