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

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Viscous fluid analogy Concept of black hole viscosity Hartle and Hawking (1972, 1973): introduced the concept of black hole viscosity when studying the response of the event horizon to external perturbations Damour (1979): 2-dimensional Navier-Stokes like equation for the event horizon =⇒ shear viscosity and bulk viscosity Thorne and Price (1986): membrane paradigm for black holes Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 21 / 38
Viscous fluid analogy Concept of black hole viscosity Hartle and Hawking (1972, 1973): introduced the concept of black hole viscosity when studying the response of the event horizon to external perturbations Damour (1979): 2-dimensional Navier-Stokes like equation for the event horizon =⇒ shear viscosity and bulk viscosity Thorne and Price (1986): membrane paradigm for black holes Shall we restrict the analysis to the event horizon ? Can we extend the concept of viscosity to the local characterizations of black hole recently introduced, i.e. future outer trapping horizons and dynamical horizons ? NB: event horizon = null hypersurface future outer trapping horizon = null or spacelike hypersurface dynamical horizon = spacelike hypersurface Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 21 / 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 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: Outline Viscous fluid analogy 1 Con
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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