Ergosphere of a Black Hole

The ergosphere of a black hole is a region on the outside of the event horizon, where spacetime itself is twisted and dragged by the forces of infinite gravitational collapse at the event horizon.

The size and shape of the ergosphere depends on the mass, rotation rate, and angular momentum of the black hole itself. This region of twisting and dragging space extends away from the event horizon at the equator, and back to the event horizon at the poles where there is zero angular momentum.

Structure of the Ergosphere

At the poles the ergosphere region actually touches the event horizon. [1] As is true with any spinning object, the exact geometric poles marked by the axis of rotation do not move spatially as they rotate — they just rotate. Thus angular momentum is zero, meaning that spacetime is not twisted and stretched at this point.

There is a precise north pole and south pole on Earth which, if you were to stand on it, you would be perfectly stationary. Slowly revolving in space, looking out at a different point in the sky as the Earth turns. Compared to someone on the equator who is actually travelling around 40,000 km every day with the rotation of the Earth, even if they do not feel it.

This is also true for black holes. They also possess an axis of rotation, and at the exact poles there is no angular momentum, so the ergosphere and event horizon are one at this point.

The ergosphere extending from the equator of a black hole has a significantly greater radius from the event horizon. At the equator angular momentum is at its maximum, so there is the greatest twisting and dragging of spacetime, which literally stretches the fabric of spacetime.

The (maximal) equatorial radius of the ergosphere of a black hole is the Schwarzschild Radius[1] — Karl Schwarzschild’s exact solution to Einstein’s Field Equations which describe the event horizon of a non-rotating black hole (which don’t actually exist in nature.

The polar (minimal) radius of the ergosphere is also the polar (minimal) radius of the event horizon — they are equal to one another. [1] For a black hole that is rotating extremely fast (therefore possessing a great deal of angular momentum) the polar (minimal) radius can be as small as half the Schwarzschild radius, while the equatorial (maximal) radius will extend out far beyond the event horizon.

Shape of the Ergosphere

A number of factors determine the exact shape and size of the ergosphere including (but not limited to) the mass of a black hole, speed of rotation, and angular momentum. The faster that a black hold rotates, the more angular momentum it has, which causes a greater dragging of spacetime at the equator (especially) causing the equatorial radius of the ergosphere to increase.

A black hole that is rotating relatively slowly will have an ergosphere that is more spherical in shape, because the ergosphere only extends modestly at the equator. The faster the rate of rotation, the more the ergosphere will extend at the equator compared to the polar proximal regions, create an oblate spheroid shape — a sphere that has been squashed slightly, so that it is shaped more like a pumpkin.

If the mass of a black hole increases, or its rate of rotation, the ergosphere will change its shape as a result.

Rotation and Radial Pull

As a black hole rotates, it twists and stretches spacetime. At the event horizon, space is pulled in the direction of rotation. It is collapsing towards singularity at the event horizon, pulling in spacetime further outside. But as you move further away from the event horizon, space is twisted less and less with greater distance (since the force of gravity decreases with distance).

As a result of this effect, spacetime is pulled at the rate of rotation at the event horizon, but at a slower rate that decreases with distance. Spacetime drags behind the further away, which is how it becomes twisted. (This is known as the Lense-Thirring Effect or frame-dragging.)