1. Exam Monday Covers reading and related notes from chapters
14.1, 14.2, 15-18, S2 & S3
Same format as last time.
One sheet of notes with writing on one side

2. Black Holes

3. Discussion
What is the equivalence principle?

5. Discussion
Explain how the equivalence principle allows accelerated motion to be relative.

8. Discussion
What are the three effects of General Relativity that we talked about last time?

9. General Theory of Relativity
Gravity is the same as the effects of acceleration, caused by a warping of spacetime
Gravity:
Slows the passage of time
Bends the path of light
Causes light to be redshifted

10. Discussion
What is Newton’s first law of motion?

11. Newton’s 1st law of motion
In the absence of net external forces, an object will travel the shortest possible path through spacetime.
The shortest path is the one for which time ticks the fastest.

12. Discussion
What does the path through spacetime look like for a skydiver in free-fall?

13. Discussion
But according to the equivalence principle, being in free-fall is exactly the same as moving at a constant velocity, far from a gravitational mass. Therefore, the skydiver, experiencing no force is traveling the shortest path through spacetime. How is this possible?

14. Dark stars
a star that has an escape velocity greater than the speed of light.

15. Discussion
Explain why “dark stars” cannot exist.

16. Schwarzschild radius
The radius at which light cannot escape from a black hole.

18. Mini-black holes?
Earth becomes a black hole if squeezed down to a radius of 9 mm.

20. Discussion
What about the light that is emitted straight up from the surface of a black hole?

21. Gravitational Redshift
Light emitted from a black hole’s Schwarzschild radius becomes infinitely redshifted.

22. Point of no return
Because Special Relativity forbids matter being accelerated to the speed of light, nothing can get out after passing the Schwarzschild radius.

23. Discussion
The Schwarzschild radius is often called the event horizon. Why do you think that is?

24. Gravitational time dilation
Gravity warps spacetime and causes clocks to tick slowly.
As you get closer to the event horizon, clocks tick slower as viewed from flat spacetime. At the event horizon a clock would cease to tick.

25. Frozen Stars
Because time stops at the event horizon, matter dropped into a black hole will never be seen to enter the black hole.

26. Discussion
If time stops at the event horizon then no matter can ever pass the event horizon and black holes can never form. Is this reasoning correct? Consider this situation from the perspective of the matter falling into the black hole. Does it see time slow? Why or why not?

27. The event horizon is not a physical boundary
Objects in free-fall feel no gravity or time dilation
It will not notice it has passed the point of no return

28. Discussion
If time stops at the event horizon of a black hole, doesn’t this mean that atoms in matter will not move and thus the temperature will reach absolute zero at the event horizon? Are black holes literally frozen?

29. Discussion
What would we need to do in order to get the time to stop for the matter?

30. You have to feel the weight to slow time

31. Three perspectives View from flat spacetime far from event horizon
Scaffold view – matter at rest with respect to the singularity near event horizon
Free-float view – matter in free fall

32. Discussion
Is it possible for us to even see the matter stuck at the event horizon? Why or why not?

33. No frozen stars
Things are not stuck on the event horizon of black holes.
Instead, the light we receive for the rest of eternity is merely echoes from the past. Light that was emitted at the event horizon will just take an infinite amount of time to reach us.

34. Discussion
If we made a black hole out of iron, and another black hole out of marshmallows, do you think there is any way we could tell the difference?

35. Black holes are all pretty much the same
Mass
Rate of spin
Electric charge

38. Frame dragging Spacetime is dragged along with a rotating black hole.
On the ergosphere, spacetime is dragged along at the speed of light.

39. Non rotating
Rotating

41. Discussion
What if the Sun suddenly collapsed into a black hole, how would this effect Earth’s orbit?

42. Black Holes don’t suck
Black holes don’t suck up all matter in the universe. At distances greater than three times the Schwarzschild radius the gravity of a black hole is the same as any other object with the same mass.

43. Discussion
According to Newton, gravity is a force that depends on the distance between masses. According to Newton what are tidal forces?

44. Discussion
Suppose two probes with the same mass are sent to explore a black hole. The first is the size of a bus, while the second is only 10 cm across. In which case will the tidal forces be the greatest? Why?

45. Discussion
In the previous question does the mass of the probes matter? Explain.

46. Discussion
Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is moving at a constant velocity how will the balls move?

47. Discussion
Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is falling freely in a gravitational field how will the balls move?

48. Discussion
Suppose you place the balls on top of each other in front of you how will they move?

49. In General Relativity Tidal forces are warped spacetime.
Space is stretched in the radial direction and squeezed in the perpendicular direction.

51. Discussion
During your trip into the black hole, where will you experience the greatest tidal forces?

52. Discussion
How could you reduce the tidal forces acting on you as you fall into a black hole?

53. Discussion
If you had to fall into a black hole would you rather fall into a solar mass black hole, or a 3 trillion solar mass black hole? Why?

54. Expedition to a singularity
Suppose we send three ships into a supermassive black hole. Santa Maria, Pinta and Nina
The ships are dropped from rest at a large distance from the black hole and allowed to free-fall in.

55. Discussion
Can the crew get any messages from home after they have passed the event horizon?

56. Discussion
Can the ships inside the black hole get any supplies from the outside?

57. Discussion
Is there any way for the ships inside the event horizon to send any messages between them?

58. Discussion
Will they be able to observe the approaching singularity in any way?

59. Discussion
Will the crew live forever?

60. Discussion
As the crew plunges in free-fall to their ultimate death near the singularity, how will they view the rest of the universe? Will they be able to see the how the universe will end? Explain.

61. Discussion
Do you think their deaths will be painful?

62. Discussion
How can we go about looking for black holes if no light can get out of them?

65. X-ray image

68. Black hole the mass of Saturn
S radius 2.8 feet

69. Simulated black hole picture

70. Discussion
Black holes are the ultimate blackbodies , or perfect absorbers. All light that shines on them is absorbed and none of it can get back out. But what happens to a perfect absorber?

72. Black holes radiate
Too little to ever be observed

73. The galactic center
Contains a strong radio source called Sagittarius A* which is likely to be a 3 million M☉ black hole.

81. The results
At the position of Sagittarius A* there must be roughly 3-4 million solar masses within the size of the solar system.
The Schwarzschild radius of a 3-4 million solar mass black hole is only 9 million km, or about 13 times the radius of the Sun.
Mercury 58 million km from Sun