Spinning Black Holes
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Transcript of Spinning Black Holes
Spinning Black Holes
•Formation
•Static Limit, Event Horizon, Cauchy Horizon
•Angular Momentum
Spinning Black HolesdT2=(1-2M/r)dt2+(4Ma/r)dtd&-dr2/(1-2M/r+a2/r2)-(1+a2/r2+2Ma2/r3)r2d&2
Equatorial Plane
Extreme Kerr (Equatorial Plane)
dT2=(1-2M/r)dt2+(4M2/r)dtd&-dr2/(1-M/r) 2-R2d&2
Where R2=r2+M2+2M3/r and & = phi
FormationFormation
3 limits ?
r Blows up at r=M± (M2-a2)0.5 t goes to zero a r=2M
dT2=(1-2M/r)dt2+(4Ma/r)dtd&-dr2/(1-2M/r+a2/r2)-(1+a2/r2+2Ma2/r3)r2d&2
Equatorial Plane
Static Limit; Event Horizon; Cauchy Horizon
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)