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Spinning Black Holes

Spinning Black Holes. Formation Static Limit, Event Horizon, Cauchy Horizon Angular Momentum. Spinning Black Holes. Extreme Kerr (Equatorial Plane) dT 2 =(1-2M/r)dt 2 +(4M 2 /r)dtd&-dr 2 /(1-M/r) 2 -R 2 d& 2.

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Spinning Black Holes

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  1. Spinning Black Holes • Formation • Static Limit, Event Horizon, Cauchy Horizon • Angular Momentum

  2. Spinning Black Holes Extreme Kerr (Equatorial Plane) dT2=(1-2M/r)dt2+(4M2/r)dtd&-dr2/(1-M/r) 2-R2d&2 dT2=(1-2M/r)dt2+(4Ma/r)dtd&-dr2/(1-2M/r+a2/r2)-(1+a2/r2+2Ma2/r3)r2d&2 Equatorial Plane Where R2=r2+M2+2M3/r and & = phi

  3. Formation

  4. 3 limits ? dT2=(1-2M/r)dt2+(4Ma/r)dtd&-dr2/(1-2M/r+a2/r2)-(1+a2/r2+2Ma2/r3)r2d&2 Equatorial Plane r Blows up at r=M± (M2-a2)0.5 t goes to zero a r=2M

  5. Static Limit; Event Horizon; Cauchy Horizon

  6. Maximum Angular Momentum r Blows up at r=M± (M2-a2)0.5 “For the case a2>M2, […] There is no black hole, and the singularity at (rho)2=0 is visible from positive infinity – i.e. there is a naked singularity. If the cosmic censorship conjecture holds, then centrifugal forces are expected to prevent the formation of a Kerr geometry with a2>M2.” P.D.D’Eath Black Holes, Gravitational Interactions (1996)

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