What happens when the collapse 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 is 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

10 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 in

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 its passed all of those tests with

flying colors and is

considered the correct theory of gravity.

We aweighed test 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 a 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

caused 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.

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.

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.