After a thorough investigation of the accretion disk around the black hole,

we'll end this module teetering at the edge of stability.

Note, we're not discussing the black hole's event horizon just yet,

but we can stay indefinitely in a stable orbit around a black hole as

long as we don't cross a boundary called the Innermost Stable Circular Orbit.

If Cygnus X-1 we're not rotating,

it would permit stable orbits about three times the distance from its event horizon.

We'll learn in module six what happens when a black hole rotates.

But this would allow stable orbits as close as

130 kilometers from the center of Cygnus X-1,

or 90 kilometers from its event horizon.

The innermost stable circular orbit is the boundary that distinguishes between

stable orbits which don't require energy for an object to stay in orbit there,

and unstable orbits which will pull you in towards the black holes event horizon.

Unless you have very powerful engines like the enterprise and Star Trek.

The innermost stable circular orbit,

which we will henceforth just call the ISCO or isco,

defines the inner edge of the accretion disk beyond which

material will fall freely and become captured by the black hole.

Somewhere between the accretion disk and the event horizon,

Newtonian gravity stops being a good approximation.

The gravitational field becomes much stronger than Newtonian gravity predicts.

This increased strength of the gravitational field is due

to corrections by Einstein's theory of general relativity.

The result is that the gravitational pull becomes much

stronger within the region bounded by the ISCO,

and stable orbits predicted by Newtonian gravity are no longer stable.

Since the gravitational potential around a black hole is

represented by a Schwarzschild potential,

there are five kinds of orbits that we can find.

There are stable and unstable circular orbits,

orbits that we call bound precessing orbits,

scattering orbits, and plunging orbits.

For a Schwarzschild black hole,

the solution to the equations of general relativity tell us the peak of the potential

occurs at a radius equal to six GM divided by c squared,

which should be looking pretty familiar right now.

Recall that we've already encountered the radius of

a Schwarzschild black hole when we were experimenting with the escape velocity formula.

The Schwarzschild radius, which describes the event horizon of a black hole,

occurs at a radius of two GM over c squared.

Quite the coincidence.

The only difference between the innermost stable circular orbit

and the event horizon is a multiple of three.

Actually, this makes life quite a bit easier for us since we can simply state

the innermost stable circular orbit of

a non-rotating black hole is three times further from the black hole's event horizon.

The key here is that it's not rotating.

We haven't discussed much about rotating black holes yet,

and we'll get more into it in module six.

But I just can't help myself here,

because the ISCO will actually change when we're considering a rotating black hole.

This is apparent in the movie Interstellar when the crew of

the Endurance visit Miller's planet very close to Gargantua's event horizon.

"Gargantua's an older spinning black hole.

It's what we call a gentle singularity.

Gentle.

They are hardly gentle. The tidal gravity is so quick that something

crossing the horizon fast might survive. A probe, say.

What happens after it crosses?

After the horizon is a complete mystery."

They were able to do it safely because a rotating black hole can

actually have an ISCO that's much closer to the event horizon.

In an extreme case,

a rotating black hole could have an ISCO coincident with the event horizon.

But we'll see more about that in an upcoming lesson.

Now, one final note about the innermost stable circular orbit.

We've only covered matter interacting with the gravitational field of the black hole.

If instead we looked at light,

we would have found a different result.

The ISCO for light orbiting a non-rotating black hole

can be a factor of two closer to the event horizon.

Photons can get trapped in circular orbits at the light ISCO radius,

and orbit many times before escaping.

We can then detect these photons,

which would look like they're coming from a sphere of light surrounding the black hole,

which scientists sometimes call the photon sphere.