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

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Local approaches to black holes Dynamics of these new horizons The trapping horizons and dynamical horizons have their own dynamics, ruled by Einstein equations. In particular, one can establish for them existence and (partial) uniqueness theorems [Andersson, Mars & Simon, PRL 95, 111102 (2005)], [Ashtekar & Galloway, Adv. Theor. Math. Phys. 9, 1 (2005)] first and second laws of black hole mechanics [Ashtekar & Krishnan, PRD 68, 104030 (2003)], [Hayward, PRD 70, 104027 (2004)] a viscous fluid bubble analogy (“membrane paradigm”, as for the event horizon) [EG, PRD 72, 104007 (2005)], [EG & Jaramillo, PRD 74, 087502 (2006)] Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 16 / 38
Local approaches to black holes Foliation of a hypersurface by spacelike 2-surfaces hypersurface H = submanifold of spacetime ⎧(M , g) of codimension 1 ⎨ spacelike H can be null ⎩ timelike H = t∈R St St = spacelike 2-surface Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 17 / 38
Page 1 and 2: 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: Local approaches to black holes Exa
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 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

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

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