The basic idea behind a dark star only requires knowledge of 18th century physics.

If a star is dense enough,

its escape velocity will be the speed of light,

making it impossible for light emitted by the star to escape the stars gravity.

The idea of a dark star,

as proposed by John Michell is not correct,

but it is still important since it introduces

some ideas that apply to black holes even in modern theories.

The problem is, that the concept of a dark star uses

Newton's older theory of gravity instead of Einstein's newer theory.

That being said, Newton's theory of gravity

is a pretty good approximation to Einstein's theory of gravity,

when gravity is weak.

It was good enough for us to plan a mission to the moon, for instance.

When I mean by weak is this,

calculate the escape velocity from a planet or star,

and compare the value of its escape velocity to the speed of light.

If the escape velocity is tiny compared to the speed of light,

then we say that gravity is weak,

and Newton's theory of gravity is a good enough approximation.

For example, the escape velocity from the Earth is 11.2 kilometers per second,

but the speed of light is approximately 27,000 times larger.

Since the escape velocity from Earth is so small compared to the speed of light,

Newton's gravity is good enough for most calculations near the surface of the Earth.

But if the escape velocity is larger,

say 10 percent of the speed of light or larger,

that means that Newton's theory of gravity is no

longer sufficient to calculate the strength of gravity.

Since Albert Einstein's equations correctly describe relativistic effects at high speeds,

they improved on Newton's theory of gravity.

This means that we can predict what happens in situations with strong gravity.

Einstein's theory of gravity is called The Theory of General Relativity.

In general relativity, mass, energy,

and angular momentum are all responsible for creating curvature in space time.

The curvature of space time then causes planets,

stars, and light to travel on curved paths.

To create a dark star,

we might start with a large star and compress it

inwards to make it smaller and denser while keeping the amount of mass unchanged.

As the star shrinks in size,

the escape velocity from the surface becomes faster

and faster until it becomes equal to the speed of light.

At this point, Newton's theory of gravity just

predicts that light won't be able to escape from the star,

and it will appear dark.

However, the predictions from Einstein's theory of

gravity demonstrate a so called dark star,

would exert a much stronger force due to gravity than predicted by Newton.

This additional inwards gravitational force

makes it impossible for a star to have a stable size.

In order for stars to exist,

there is a delicate balance between its gas molecules,

which exert a net outwards pressure

that is exactly balanced by the attraction of gravity,

allowing stars to stay the same size over time.

When a star gets so small,

that its escape velocity is the speed of light,

then the required outward gas pressure is infinite.

There is no way to create infinite gas pressure,

so the star is unstable and begins collapsing inwards.

A black hole is what remains after a star is unable to resist gravity and collapses inwards.

A black hole does not have a surface but there is

a special boundary that surrounds a black hole called an event horizon.

In the case of the simplest black hole,

the event horizon is a sphere with a radius called

the Schwarzschild radius with the value,

event horizon radius equals 2 times G,

times the mass of the black hole,

divided by the speed of light squared.

The amazing thing about the formula for

the event horizon radius is that it is

exactly the same equation that Michell derive for the radius of a dark star.

The event horizon radius is a boundary for light rays.

If an astronaut shines a flashlight outside of the event horizon,

the light rays can escape and be seen by astronomers far away from the black hole.

But if the flashlight is at or inside of the event horizon,

all light emitted will be trapped inside of a black hole. And it's not just light,

massive objects like cakes,

or rockets, or astronauts,

can escape as long as they are outside of

the event horizon radius and their rocket is good enough.

But if a cake eating astronaut crosses the boundary defined by black holes event horizon,

no escape is possible.

The name black hole didn't enter a common usage until 1967,

where it was popularized by John Wheeler.

Before then, astronomers used the name

Totally Gravitationally Collapsed Objects to describe black holes.

This is an accurate phrase,

but difficult to say.

So it's not surprising that the name black hole caught on

so quickly with scientists and science fiction writers alike.