Spinning black holes

So far I have restricted myself to discussing the simplest kind of
black hole: one that is described by the Schwarzschild solution of
Einstein’s field equations. This is really only an idealized scenario.
A real black hole would be spinning too. We know that stars spin
about their axis in the same way that the Earth does. Therefore
when they collapse they will spin even faster. Let us examine
briefly why this should be so.
An important quantity in physics is known as angular
momentum and is possessed by all rotating objects. The reason
it is so important is that it is one of those quantities, like energy,
that is said to be conserved, which means it stays the same provided
the rotating object is not subjected to an external force. Angular
momentum depends on the mass of the object, the rate it is
spinning and its shape. Think of an ice skater spinning with her
arms extended outwards. Asshe brings her arms closer to her body
and folds them against her chest, she will spin faster. The reason
for this is that her angular momentum must remain constant—
ignoring friction of the blades on the ice—and, by bringing her
arms in, she has altered her shape which would reduce her angular
momentum if this were all that happens. However, she will also
spin faster to compensate for this and keep her angularmomentum
the same. This increase in the rate at which she spins is not
something that she does deliberately; it happens automatically.
Aren’t the laws of physics clever? A collapsing spinning star
behaves in the same way: its reduced size must be countered by it
spinning faster in order to maintain its angular momentum.According to Newton’s version of gravity we cannot tell the difference between the gravitational effects of a spinning spherical object and one that is not spinning (as long as it does not wobble
about as it spins). Here again, general relativity is different. A
spinning black hole literally drags space around it to form a gravitational
vortex, rather like the way water circles round a plughole.
In such a region of space an orbiting body would have to accelerate
in the opposite direction to the spin of the black hole just to stand
still! This strange result provides us with a means of measuring
the rate at which a black hole is spinning which, along with its
mass (from which we can deduce its size), is the only other quantity
there is to describe all we can about a black hole6. To measure
the spin of a black hole we need to put two satellites into orbit in
opposite directions around it. Since the satellite that is orbiting in
the opposite direction to the black hole’s spin must move ‘against
the tide’ of moving space, it will take longer to complete one full
orbit since by covering more space it has travelled further. The difference
in orbit times between the satellites tells us the rate of spin.
This region where space is dragged round a spinning black
hole is called the ergosphere. It means that a spinning black hole
will have two horizons: an inner, spherical, one which is the
original event horizon and from which nothing can escape and
an outer, bulged-out at the equator one which marks the surface
of the ergosphere (figure 4.2). Within the ergosphere, the dragging
is so strong that nothing can stand still. However, an object that
falls into the ergosphere can still escape again, as long as it does
not stray within the event horizon.