Black holes: from event horizons to trapping horizons - LUTH ...
Black holes: from event horizons to trapping horizons - LUTH ... Black holes: from event horizons to trapping horizons - LUTH ...
Local approaches to black holes Normal null frame associated with the evolution vector The foliation (St)t∈R entirely fixes the ambiguities in the choice of the null normal frame (ℓ, k), via the evolution vector h: there exists a unique normal null frame (ℓ, k) such that h = ℓ − Ck and ℓ · k = −1 Normal fundamental form: Ω (ℓ) := −k · ∇q ℓ or Ω (ℓ) α := −kµ∇νℓ µ q ν α Evolution of h along itself: ∇hh = κ ℓ + (Cκ − Lh C)k − DC NB: null limit : C = 0, h = ℓ =⇒ ∇ℓℓ = κ ℓ =⇒ κ = surface gravity Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 19 / 38
Outline Viscous fluid analogy 1 Concept of black hole and event horizon 2 Local approaches to black holes 3 Viscous fluid analogy 4 Angular momentum and area evolution laws 5 Applications to numerical relativity Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 20 / 38
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Outline<br />
Viscous fluid analogy<br />
1 Concept of black hole and <strong>event</strong> horizon<br />
2 Local approaches <strong>to</strong> black <strong>holes</strong><br />
3 Viscous fluid analogy<br />
4 Angular momentum and area evolution laws<br />
5 Applications <strong>to</strong> numerical relativity<br />
Eric Gourgoulhon (<strong>LUTH</strong>) <strong>Black</strong> <strong>holes</strong>: <strong>trapping</strong> <strong>horizons</strong> CERN, 17 March 2010 20 / 38
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