Spin is a source of free energy up to 29 of energy for

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Unformatted text preview: as velocity: dφ v=r = GM / r dt !! •  Now, for photons on circular, equatorial orbit ds=__, dr=__, θ=π/2 & dθ=__. So, € 2 # 2& 0 = %cdt 1 − 2GM / rc ( − rdφ ' !! $ •  Combining these equa8ons: () 2 € 4/9/2013 UW, ASTR 323, SP13, Eric Agol ©2013 9 4/9/2013 UW, ASTR 323, SP13, Eric Agol ©2013 10 Geometry Near Black Hole Marginally stable circular orbit γ Circular photon orbit i Marginally stable orbit, Rms, equatorial radius within which no stable circular marer orbits exist Rms=__ rg for as=0, Rms=__ rg for as=1 i Photon circular orbit, Rph, unstable - radius is Rph = 3rg for as=0, Rph=1rg for as=1 i A spinning black hole drags space with it. Spin is a source of free energy - up to 29% of energy for as=1. 4/9/2013 UW, ASTR 323, SP13, Eric Agol ©2013 11 Effect of black holes on light & marer •  Gravita8onal redshiu/8me...
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This document was uploaded on 04/05/2014.

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