1. Special Relativity -- The Genius of Einstein

Special Relativity applies when objects move at speeds appreciable to the speed of light.

- speed of light is finite

- yet, speed of light is measured to be the same for every observer

(This is an observed fact: The Michelson-Morely experiment)

What happens when one observer is moving at a speed close to that of light relative to another observer?

How is time measured?

How are lengths measured?

Answer: Through the transmittal of information via light

Consequence: Each observer sees the other observer get shorter (in the direction of motion) and the other's clock slow down.

Space and time (3+1 dimensions) are not seperate quantities, but form a 4-dimensional spacetime

2. Now Add Gravity - General Relativity

Special Relativity deals with objects moving in the absence of gravity

What happens when you add gravity?

Elevator thought experiment:

Gravity is indistinguishable from an acceleration

Postulate: gravity even effects light (photons)

i.e. it accelerates them, or deflects their paths

Gravity warps spacetime - gravity produces a "curavture" to spacetime.

Acceleration is when an object resists curvature.

3. Gravity taken to extremes

If some local region of spacetime is warped enough, it pinches off

This means that the curvature of spacetime is so great, even light cannot escape

This region of spacetime collapses infinitely into a singularity

This is a black hole

How does spacetime get warped?

Because there is mass present which produces a gravitational field

For every mass there is a escape velocity which depends on distance from the mass.

For a black hole, there is a event horizon which is the distance where the escape velocity is the speed of light.

Another name for the event horizon:

Schwarzschild radius (R_S)

R 3 km (M/M)

The bigger the mass, the bigger the event horizon.

What's inside the event horizon?

4. Super massive black holes

The typical size of a typical galaxy is about 30,000 pc

100,000 ly

9.3 x 10¹⁷ km

So, for a 10⁶ to 10⁹ M black hole,

the event horizon is only 3 x 10⁶ to 3 x 10⁹ km

- puny compared to the galaxy

We believe that in the center of most galaxies there exists a massive black hole of order these masses.

How do we know?

5. Gravity, black holes, and the Universe

So what happens if all of spacetime is warped enough to pinch off?

How would we know if our Universe is like that?

First note that the event horizon scales with mass

But for a uniform density, mass scales with size³

That means that the larger the "black hole," the less dense it has to be

In other words, you don't have to have a singularity to have a "black hole"

What is the critical average density of the Universe for it to be a black hole?

. . . we'll re-explore this in Lecture 42.

(a) Nothing moves faster than the speed of light

(b) All observers measure the speed of light to be the same

(c) Gravity affects everything, including light

(d) light travels faster in gravitational fields

(e) Gravity warps spacetime