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

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Local approaches <strong>to</strong> black <strong>holes</strong><br />

Evolution vec<strong>to</strong>r on the horizon<br />

Vec<strong>to</strong>r field h on H defined by<br />

(i) h is tangent <strong>to</strong> H<br />

(ii) h is orthogonal <strong>to</strong> St<br />

(iii) Lh t = h µ ∂µt = 〈dt, h〉 = 1<br />

NB: (iii) =⇒ the 2-surfaces St are Lie-dragged<br />

by h<br />

Eric Gourgoulhon (<strong>LUTH</strong>) <strong>Black</strong> <strong>holes</strong>: <strong>trapping</strong> <strong>horizons</strong> CERN, 17 March 2010 18 / 38

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