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)