uw astr 323 sp13 eric agol 2013 2 s 6 schwarzschild

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Unformatted text preview: sphere of no return (aka event horizon) 4/9/2013 UW, ASTR 323, 25, 2009 #5 gol ©2013 Feb SP13, Eric A Black hole proper8es i Mass (M), Charge (Q≈0), and Spin (as=Jc/GM2, 0 < as < 1) i Gravita8onal radius: rg=______ i Event Horizon: sphere surrounding singularity within which escape speed > c 4/9/2013 ( rH = rg 1 + 1 - a !! UW, ASTR 323, SP13, Eric Agol ©2013 2 s ) 6 Schwarzschild metric •  In flat space: (ds = cdt − dr − rdθ − r sinθdφ ) !! ) ( ) ( ) ( ) ( •  In curved space around black hole of mass M distances in 8me & space can be a func8on of the € coordinates 2 2 2 2 2 # &2 2 2 dr # ( − rdθ − r sinθdφ %cdt 1 − 2GM / rc 2 & − % ( ds = $ ' % 1 − 2GM / rc 2 ( $ ' !! () 2 ()( ) 2 •  Light always has ds= __ ; space- 8me distances between objects (or events) are measured by € integra8ng ds, not by integra8ng between coordinates 4/9/2013 UW, ASTR 323, SP13, Eric Agol ©2013 7 Gravita8onal lensing •  Photons are bent by gravity: 4/9/2013 UW, ASTR 323, SP13, Eric Agol ©2013 8 Photon circular orbit •  A circular orbit h...
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