Fall 2000 ASTR 1120-001 Review for Quiz 4

The quiz will contain 10 multiple-choice questions, and will be 10 minutes long. The intention is that all material on the quiz (saving matters of logic and common sense) is referred to somewhere here.

Section S3 of Jeff Bennett's book covers special relativity in more detail than we have been able to cover. Section S4 covers general relativity, with a slightly different emphasis than ours: Jeff empasizes the equivalence principle and curvature, whereas we have emphasized the phenomenology of black holes, wormholes, and Hawking radiation.

You can ask about the answers in the review session at 7-7:50pm on Monday 30 October in Duane G1B30 (our usual lecture hall).

1. Postulates of Special Relativity. Special Relativity can be derived mathematically from a number of postulates. The most important of these is that ``the speed of light c is the same for all observers''.

2. Consequences of Special Relativity. The assumption of the constancy of the speed of light is inconsistent with the classical Galilean concept of absolute space and time, which would predict that different observers would observe light moving at different velocities, depending on their motion through the `aether'. The assumption that the speed of light is constant implies that observers moving relative to each other must measure space and time differently. See paradox. Time dilation: you think the clock on someone moving relative to you runs slower than your own clock. Lorentz contraction: you think that someone moving relative to you is contracted along the direction of motion. Other consequences of the constancy of the speed of light are: The speed of light is an absolute speed limit - nothing can move faster than the speed of light. Mass and energy are equivalent, the famous E = m c2.

3. How things look when you travel near the speed of light. Describe how things look if you travel near the speed of light. See Special Relativistic Flight Simulators.

4. Evidence for Relativistic Motion in Cosmic Jets. Cosmic jets are observed emerging from the centers of some galaxies. In many cases these jets are one-sided, and in some cases, such as the galaxy M87 or the quasar 3C273, jets show superluminal (faster than light) motion. Explain how these two phenomena are interpreted as indicating that the jets are moving close to the speed of light.

5. Black Hole. What is a black hole? What is it made of?

6. Schwarzschild Radius. How do you spell Schwarzschild? The Schwarzschild radius of a black hole of mass M is RSch = 2 G M / c2. What is the significance of the Schwarzschild radius? What is the horizon of a black hole? If you, an outsider, observed photons emitted from just outside the Schwarzschild radius, how would those photons appear? What happens to time near the Schwarzschild radius (a) as observed by an outside observer, (b) as observed by someone actually there, near the Schwarzschild radius? See Schwarzschild.

7. Gravitational Redshift. What is the gravitational redshift? Explain how the gravitational redshift comes about, given the concepts that photons have energy, and that objects lose (gain) energy when climbing out of (falling into) a gravitational potential. See Schwarzschild.

8. Friend falls into a Black Hole. You watch a friend fall into a black hole. Describe what you see. See orbit.

9. You fall into a Black Hole. You fall into a black hole. Describe what you see and experience. See singularity.

10. X-Ray Binaries. What is an x-ray binary? What is an accretion disk? What produces the x-rays? What heats the material to the point where it emits x-rays? What evidence might suggest that the compact object in an x-ray binary is a neutron star or black hole? See Mitch Begelman's Binaries and Accretion Disks.

11. Observational evidence for Black Holes. If black holes are black, how can you tell if one is there? What is the evidence which suggests that Cygnus X-1 contains a black hole? What is the evidence which suggests that galaxies like M87, or quasars like 3C273, contain black holes at their centers?

12. Wormholes. General relativity allows the mathematical existence of `wormholes' connecting separate regions of space. Do wormholes exist in reality? Describe some of the problems involved in their actual existence. Why is it not possible to travel through a wormhole? Is a wormhole stable? To make a wormhole traversable and stable requires `exotic matter'. What is exotic matter? See wormholes.

13. Hawking Radiation. What is Hawking radiation? How is the temperature of Hawking radiation related to the size of a black hole? What is the Hawking luminosity of a black hole? Typically, is the Hawking temperature and Hawking luminosity of an astronomical black hole large or small? See Hawking.