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 ...
Angular momentum and area evolution laws Angular momentum flux law Under the supplementary hypothesis that ϕ is transported along the evolution vector h : Lh ϕ = 0, the generalized Damour-Navier-Stokes equation leads to d J(ϕ) = − T (m, ϕ) dt S ɛ − 1 σ 16π (m) : Lϕ q − 2θ (k) ϕ · DC Sɛ St St [EG, PRD 72, 104007 (2005)] Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 33 / 38
Angular momentum and area evolution laws Angular momentum flux law Under the supplementary hypothesis that ϕ is transported along the evolution vector h : Lh ϕ = 0, the generalized Damour-Navier-Stokes equation leads to d J(ϕ) = − T (m, ϕ) dt S ɛ − 1 σ 16π (m) : Lϕ q − 2θ (k) ϕ · DC Sɛ St Two interesting limiting cases: St [EG, PRD 72, 104007 (2005)] Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 33 / 38
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- Page 43 and 44: Outline Viscous fluid analogy 1 Con
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Angular momentum and area evolution laws<br />
Angular momentum flux law<br />
Under the supplementary hypothesis that ϕ is transported along the evolution<br />
vec<strong>to</strong>r h : Lh ϕ = 0, the generalized Damour-Navier-S<strong>to</strong>kes equation leads <strong>to</strong><br />
<br />
d<br />
J(ϕ) = − T (m, ϕ)<br />
dt S ɛ − 1<br />
<br />
σ<br />
16π<br />
(m) : Lϕ q − 2θ (k) <br />
ϕ · DC<br />
Sɛ<br />
St<br />
Two interesting limiting cases:<br />
St<br />
[EG, PRD 72, 104007 (2005)]<br />
Eric Gourgoulhon (<strong>LUTH</strong>) <strong>Black</strong> <strong>holes</strong>: <strong>trapping</strong> <strong>horizons</strong> CERN, 17 March 2010 33 / 38
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