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 "curvature" 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 3 km (M_BH/M)

The bigger the black-hole mass (M_BH), the bigger the event horizon.

What's inside the event horizon?

4. Gravity, black holes, and the Universe

What's inside the event horizon?

• How do we know we are not living inside a titanic black hole?
• This is the same as asking: What happens if all of spacetime is warped enough to pinch off?
• How would we know if our Universe is like that?

First recall that the event horizon scales with black hole mass, M_BH:

R_S 3 km (M_BH/M)

But for a uniform density, mass scales with size, cubed:

mass   =   density   x   volume

volume   =   (4 / 3) R_S³     M_BH³

  density     M_BH^-2

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 mean density of the Universe for it to be a black hole?

. . . we'll re-explore this in Lecture 27.

5. Super massive black holes in galaxies

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 (R_S) 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?

6. Black holes in action: Active Galaxies

Define:

Galaxies with nuclei (centers) that are overly luminous, and have emission indicative of a non-thermal source.

non-thermal: not a black-body

(i.e not stars, or not just stars)

What, then, causes this luminosity?

The Central Engine

(i) The facts:

• AGN have high luminosities, typically larger than 'normal' galaxies (like the Milky Way).

  - most of this emission is at infrared and radio wavelengths

• energy emission is non-stellar (non-thermal)

  - spectral continuum is NOT shaped like a black-body
  - continuum radio emission is largely due to electrons spinning in magnetic fields:

  ``synchotron'' radiation

• energy emission is variable on time-scales of one year or less.

  - objects rapidly get brighter and fainter

  small sizes

  (of order a light-year in size)

• AGN often are associated with jets of material extending over large distances (up to a Mpc or so)

  - a powerful engine!

• spectra show broad emission-lines that indicate rapid internal motions in the energy-producing region

  - a massive engine!

(ii) The speculations:

Could the central engine consist of . . .

(a) an incredibly massive star?

Possibly, but it would burn up quickly and lead to a massive black hole.

(b) many very massive stars?

Possibly, but they would burn up quickly and lead to many black holes that would eventually collapse into a single massive black hole.

Also, neither of the above cases naturally produce the right time variability, jets, and large non-thermal emission.

(c) a massive black hole surrounded by a hot, glowing accretion disk fed by in-falling material

fits the bill!

• small size
  rapid variability

  hot accretion disk, with magnetic fields and lots of free electrons

  non-thermal emission

  jets

  massive = powerful

  high luminosity (a little fuel goes a long way)

(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

(a) radiation is non-thermal.

(b) central luminosities vary on rapid time-scales.

(c) some AGN have jets.

(d) some AGN have strong radio emission.

(e) some AGN are in spiral galaxies.