What happens when the collapsed remnant of a giant star at the end of its life is

more than three times the mass of the Sun?

Under this situation, there's no force of nature that can resist the continued

collapse, not electron degeneracy pressure, not neutron degeneracy pressure.

In principle, the stellar remnant must continue to collapse to a state whose

properties are as bizarre as any state of matter in the universe, a black hole.

To understand black holes fully, we'd have to delve into Einstein's general theory of

relativity, a complex and difficult theory involving tensors and

ten coupled second-order partial differential equations.

Since that level of math is beyond the scope of this course,

we'll just approach black holes in a conceptual way.

Remember that for weak situations of gravity, which is most of the universe,

general relativity produces the same predictions as Newton's theory.

But when gravity is strong, it gives much better results, and for some phenomena,

they are simply not predicted or understood in terms of Newton's theory.

The mathematics and the theory of general relativity are difficult enough

that only a handful of very particular situations have been solved fully.

The full description of space-time and general relativity is called a metric, and

only a handful of metrics have been solved in the 60 or

70 years that people have been doing this research.

It's very hard to do real-world problems.

So most of the solutions are for very artificial cases,

such as a black hole that's not spinning or a black hole that's spinning.

Einstein's theory has only been tested in the weak field case,

such as with its confirmation in the eclipse of the Sun in 1916.

But it's passed all of those tests with flying colors and

is considered the correct theory of gravity.

We await tests of gravity in the strong field situation or for

the predictions that are unique to the general theory of relativity and

do not occur in Newtonian gravity.

The central conceptual shift in general relativity is the idea that space and

time are curved by mass and energy.

Mass and energy are themselves equivalent by Einstein's other insight,

E equals mc squared.

It's, of course, difficult to visualize the curvature of space-time

in three dimensions when we occupy three dimensions, so

we tend to use analogies in two dimensions or visualizations.

The commonly used visualization involves the two-dimensional

analogy of a flat sheet made of rubber.

In Newtonian theory, the sheet is always flat, and

mass objects sit in the sheet without distorting it or changing its properties.

In general relativity, any mass, or a combination of mass and

energy, distorts the sheet, which is the space-time continuum.

And objects traveling through that space-time follow paths determined by

the curvature of the space-time.

We can think of ball bearings or marbles rolled over

a rubber sheet that has depressions in it causes by the mass in space.

The higher the mass energy density, the higher the curvature of space.

This is the central equivalence of Einstein's theory.

In principle, there can be sufficient mass energy density

to pinch off space entirely, trapping a region of space-time beyond the view

of the rest of the space time and removing it from the visible universe.

This in essence is a black hole.

Another way to think of black holes is by simple extrapolation or

extension of Newton's theory.

And in fact, John Michell in 1795, using purely Newtonian theory,

made a prediction of black holes and their existence.

He just extrapolated from the terrestrial situation where the escape velocity for

any object is 11 kilometers per second.

From the Sun, the escape velocity is 600 kilometers per second.

He recognized that there might be a mass, or

in particular, a very high density form of mass, where the escape velocity at

the surface would naturally reach 300,000 kilometers per second, the speed of light.

By analogy and by extrapolation,

this would be a situation where nothing could escape, not even light.

Although the analogy is not correct because we have to use general relativity

to understand black holes, the concept is correct.

Nothing can leave the event horizon of a black hole.

The event horizon is not a physical barrier.

It's a mathematical description of the place that defines where information is

trapped forever.

Essentially, it's an information membrane.