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

More documents

Recommendations

Info

Angular momentum and area evolution laws Area evolution law for an event horizon A(t) : area of the 2-surface St; S ɛ : volume element of St; ¯κ(t) := 1 κ A(t) St S ɛ Integrating the null Raychaudhuri equation on St, one gets d2 A − ¯κdA = − dt2 dt 8πT (ℓ, ℓ) + σ (ℓ) :σ (ℓ) − (θ(ℓ) ) 2 2 + (¯κ − κ)θ(ℓ) S ɛ (1) St [Damour, 1979] Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 34 / 38
Angular momentum and area evolution laws Area evolution law for an event horizon A(t) : area of the 2-surface St; S ɛ : volume element of St; ¯κ(t) := 1 κ A(t) St S ɛ Integrating the null Raychaudhuri equation on St, one gets d2 A − ¯κdA = − dt2 dt 8πT (ℓ, ℓ) + σ (ℓ) :σ (ℓ) − (θ(ℓ) ) 2 2 + (¯κ − κ)θ(ℓ) S ɛ (1) St Simplified analysis : assume ¯κ = const > 0 : Cauchy problem =⇒ diverging solution of the homogeneous equation: dA = α exp(¯κt) ! dt [Damour, 1979] Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 34 / 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 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14: 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 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 63: Angular momentum and area evolution
Page 69 and 70: Outline Applications to numerical r
Page 71: Review articles References A. Ashte
show all

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

Create successful ePaper yourself

Delete template?

Save as template?