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 ...
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Local approaches <strong>to</strong> black <strong>holes</strong><br />
What is a trapped surface ?<br />
2/ The definition<br />
S : closed (i.e. compact without boundary) spacelike 2-dimensional surface<br />
embedded in spacetime (M , g)<br />
Being spacelike, S lies outside the light<br />
cone<br />
∃ two future-directed null directions<br />
orthogonal <strong>to</strong> S:<br />
ℓ = outgoing, expansion θ (ℓ)<br />
k = ingoing, expansion θ (k)<br />
In flat space, θ (k) < 0 and θ (ℓ) > 0<br />
S is trapped ⇐⇒ θ (k) < 0 and θ (ℓ) < 0 [Penrose 1965]<br />
S is marginally trapped ⇐⇒ θ (k) < 0 and θ (ℓ) = 0<br />
Eric Gourgoulhon (<strong>LUTH</strong>) <strong>Black</strong> <strong>holes</strong>: <strong>trapping</strong> <strong>horizons</strong> CERN, 17 March 2010 11 / 38
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