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 ...
Viscous fluid form Viscous fluid analogy S Lh π + θ (h) π = −DP + 1 8π D · σ(m) + ζDθ (h) + f with π := − 1 8π Ω(ℓ) momentum surface density P := κ 8π pressure 1 8π σ(m) shear stress tensor ζ := 1 bulk viscosity 16π f := −q ∗ T · m + θ(k) DC external force surface density 8π Similar to the Damour-Navier-Stokes equation for an event horizon, except the Newtonian-fluid relation between stress and strain does not hold: σ (m) /8π = 2µσ (h) , rather σ (m) /8π = [σ (h) + 2Cσ (k) ]/8π Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 30 / 38
Viscous fluid form Viscous fluid analogy S Lh π + θ (h) π = −DP + 1 8π D · σ(m) + ζDθ (h) + f with π := − 1 8π Ω(ℓ) momentum surface density P := κ 8π pressure 1 8π σ(m) shear stress tensor ζ := 1 bulk viscosity 16π f := −q ∗ T · m + θ(k) DC external force surface density 8π Similar to the Damour-Navier-Stokes equation for an event horizon, except the Newtonian-fluid relation between stress and strain does not hold: σ (m) /8π = 2µσ (h) , rather σ (m) /8π = [σ (h) + 2Cσ (k) ]/8π positive bulk viscosity This positive value of bulk viscosity shows that FOTHs and DHs behave as “ordinary” physical objects, in perfect agreement with their local nature Eric Gourgoulhon (LUTH) Black holes: trapping horizons CERN, 17 March 2010 30 / 38
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Viscous fluid form<br />
Viscous fluid analogy<br />
S<br />
Lh π + θ (h) π = −DP + 1<br />
8π D · σ(m) + ζDθ (h) + f<br />
with π := − 1<br />
8π Ω(ℓ) momentum surface density<br />
P := κ<br />
8π pressure<br />
1<br />
8π σ(m) shear stress tensor<br />
ζ := 1<br />
bulk viscosity<br />
16π<br />
f := −q ∗ T · m + θ(k)<br />
DC external force surface density<br />
8π<br />
Similar <strong>to</strong> the Damour-Navier-S<strong>to</strong>kes equation for an <strong>event</strong> horizon, except<br />
the New<strong>to</strong>nian-fluid relation between stress and strain does not hold:<br />
σ (m) /8π = 2µσ (h) , rather σ (m) /8π = [σ (h) + 2Cσ (k) ]/8π<br />
positive bulk viscosity<br />
This positive value of bulk viscosity shows that FOTHs and DHs behave as<br />
“ordinary” physical objects, in perfect agreement with their local nature<br />
Eric Gourgoulhon (<strong>LUTH</strong>) <strong>Black</strong> <strong>holes</strong>: <strong>trapping</strong> <strong>horizons</strong> CERN, 17 March 2010 30 / 38
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