A black hole is described by its mass $M$, angular momentum per unit mass $a$, electric charge $Q$ and magnetic charge $P$. However the essential features persist in the absence of charges, so a rotating black hole $(M, a)$ as described by the Kerr metric is representative of cosmological black holes.

The outer event horizon in Kerr is given by
$$r_+ = M + \sqrt{M^2 -a^2}$$ where:
$c = G = 1$ natural units
$(t, r, \theta, \phi) =$ Boyer-Lindquist coordinates
$a = J/M$
$J =$ angular momentum

A stationary observer $(r, \theta = constant)$ ideally on the event horizon is co-rotating with the black hole at angular velocity $\Omega = a / (r_+^2 + a^2)$.

The event horizon exists if $a \le M$. If $a \gt M$ the Kerr solution describes a naked singularity, however it is believed that is not physical. Reason being that in a gravitational collapse of a rapidly rotating object the centrifugal forces can prevent the formation of a black hole.

At the limit $a = M$ the black hole angular velocity is
$$\Omega_{max} = 1 / (2M)$$ Note: $\Omega$ is monotonically increasing in the interval $0 \lt a \lt M$.

A black hole is described by its mass $M$, angular momentum per unit mass $a$, electric charge $Q$ and magnetic charge $P$. However the essential features persist in the absence of charges, so a rotating black hole $(M, a)$ as described by the Kerr metric is representative of cosmological black holes.

The outer event horizon in Kerr is given by
$$r_+ ~=~ M + \sqrt{M^2 -a^2} \,,$$ where:

• natural units are used such that $c = G = 1$;

• $\left(t, r, \theta, \phi \right) =$ Boyer-Lindquist coordinates;

• $a = \frac{J}{M}$;

• $J =$ angular momentum .

A stationary observer $(r, \theta = \text{constant})$ ideally on the event horizon is co-rotating with the black hole at angular velocity $\Omega = a / \left(r_+^2 + a^2\right)$.

The event horizon exists if $a \le M$. If $a \gt M$ the Kerr solution describes a naked singularity, however it is believed that is not physical. Reason being that in a gravitational collapse of a rapidly rotating object the centrifugal forces can prevent the formation of a black hole.

At the limit $a = M$ the black hole angular velocity is
$$\Omega_{\text{max}} = \frac{1}{2M} \,.$$ Note that $\Omega$ is monotonically increasing in the interval $0 \lt a \lt M$.

A black hole is described by its mass $M$, angular momentum per unit mass $a$, electric charge $Q$ and magnetic charge $P$. However the essential features persist in the absence of charges, so a rotating black hole $(M, a)$ as described by the Kerr metric is representative of cosmological black holes.

The outer event horizon in Kerr is given by
$r_+ = M + \sqrt{M^2 -a^2}$
where:
$c = G = 1$ natural units
$(t, r, \theta, \phi)$ Boyer-Lindquist coordinates
$a = J/M$
$J$ angular momentum

A stationary observer $(r, \theta = constant)$ ideally on the event horizon is corotating with the black hole at angular velocity $\Omega = a / (r_+^2 + a^2)$.

The event horizon exists if $a \le M$. If $a \gt M$ the Kerr solution describes a naked singularity, however it is believed that is not physical. Reason being that in a gravitational collapse of a rapidly rotating object the centrifugal forces can prevent the formation of a black hole.

At the limit $a = M$ the black hole angular velocity is
$\Omega_{max} = 1 / (2M)$
Note: $\Omega$ is monotonically increasing in the interval $0 \lt a \lt M$.

A black hole is described by its mass $M$, angular momentum per unit mass $a$, electric charge $Q$ and magnetic charge $P$. However the essential features persist in the absence of charges, so a rotating black hole $(M, a)$ as described by the Kerr metric is representative of cosmological black holes.

The outer event horizon in Kerr is given by
$$r_+ = M + \sqrt{M^2 -a^2}$$ where:
$c = G = 1$ natural units
$(t, r, \theta, \phi) =$ Boyer-Lindquist coordinates
$a = J/M$
$J =$ angular momentum

A stationary observer $(r, \theta = constant)$ ideally on the event horizon is co-rotating with the black hole at angular velocity $\Omega = a / (r_+^2 + a^2)$.

The event horizon exists if $a \le M$. If $a \gt M$ the Kerr solution describes a naked singularity, however it is believed that is not physical. Reason being that in a gravitational collapse of a rapidly rotating object the centrifugal forces can prevent the formation of a black hole.

At the limit $a = M$ the black hole angular velocity is
$$\Omega_{max} = 1 / (2M)$$ Note: $\Omega$ is monotonically increasing in the interval $0 \lt a \lt M$.