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ASTR 3740 Relativity & Cosmology Spring 2021 Problem Set 3: Questions you posed.

  1. Could a collapsing star create a wormhole?
  2. If infalling matter appears to freeze at the horizon, then how does a black hole gain mass?
  3. If the Milky Way has a supermassive black hole at its center, why aren't we all pulled into it?
  4. An isolated black hole has a finite temperature, the Hawking temperature. Does this mean that light is escaping from inside a black hole?
  5. In the movie Interstellar, one hour on Miller's planet is said to be 7 years on Earth. Is this a reasonably possible time dilation for a planet closely orbiting Gargantua, a black hole of 100 million solar masses?
    Near the singularity
  1. You and your friend fall into a black hole at same time but from different positions, so you reach the singularity at the same time. Assuming you can withstand the tidal forces, do you and your friend have a chance to meet and shake hands at the singularity?
  2. If you fall inside the horizon to the singularity of a Schwarzshild black hole, do you see a naked singularity approaching you?
  3. Two friends jump into a black hole at the same time, from two separate diving boards 10 meters apart. As the friends fall in and watch each other, what do they see?
  4. You and a friend fall inside the horizon of a black hole. Can you communicate with your friend?
  5. When you fall to the singularity of a black hole, why does it look like you are falling on to a plane, as opposed to a hole or a sphere?
  6. Why do spinning black holes have a ring singularity instead of a point singularity?

    7. Wormhole
  7. An Einstein-Rosen bridge connects the horizons of a black hole and white hole, and ultimately connects two universes. If you were to enter an Einstein-Rosen bridge, would you be able to travel between the two universes?
  8. If you fall into a white hole, will you be able to send back a signal to the universe you came from?

    9. Tidal forces
  9. If you fall into a black hole, would you notice when you passed through the horizon?
  10. As you fall into a black hole, the tidal forces pull you apart vertically and crush you horizontally. How do these tidal forces affect your view of the Universe as you approach the singularity?
  11. As you fall through the horizon of a black hole of one billion solar masses, do you get ripped apart by tidal forces?
  12. Is there any kind of black hole whose horizon you could cross without being ripped apart by tidal forces?

    13. Appearance
  13. Black holes trap light, and cannot be seen. How then do astronomers observe black holes?
  14. Someone falls into a black hole 100 years before you do. Do you see them still falling in, even after all that time?
  15. You hover a long distance from a black hole, using rockets to counteract the gravity. You let go of a flashlight, and watch it free-fall into the black hole. Describe the appearance of the flashlight as it falls.
  16. You and a friends are on opposite sides of a black hole. Can you see each other?
  17. On your way back to your home planet after traversing the Universe, you find a black hole on a direct line between you and your planet! What does your planet look like as you approach the black hole?
  18. If you free-fall into a Schwarzschild black hole, does the scene above and below appear redshifted or blueshifted?
  19. If you fall into a black hole, does the surrounding scene appear redshifted or blueshifted?
  20. As we approach a black hole close to a star, the star appears to distort and split apart. Is this because the star is torn apart by the black hole?

    21. Orbits
  21. At the photon sphere, 1.5 Schwarzschild radii, light orbits in circles about a black hole. Can light orbit a black hole at larger radii?
  22. If the closest stable orbit to a black hole is 3 Schwarzschild radii, how close can you safely orbit a black hole?
  23. True or false: Orbiting near a black hole for some time can have gravitational time dilation effects similar to relativistic time dilation from traveling near the speed of light.
  24. True or false: Time near a black hole appears to go slower because you are moving near the speed of light, so time is dilated.
  25. Is the trajectory into a black hole a straight line or a swirl?

    26. Hawking radiation
  26. Is it likely that an astronomical black hole has evaporated by Hawking radiation since the start of the Universe?
  27. How much energy per second does a stellar-mass black hole give off in Hawking radiation?

    28. Description
  28. Describe the phenomenon of gravitational lensing.
  29. What does it mean to say that “a black hole has no hair”?
  30. What is the difference between a Schwarzschild black hole and a Kerr black hole?
  31. What is a Reissner-Nordström black hole, and can they exist in reality?
  32. What is the difference between a Schwarzschild black hole and a Reissner-Nordström black hole?
  33. What are some differences between a Schwarzschild black hole and a Reissner-Nordström black hole?
  34. How does the Schwarzschild radius of a supermassive black hole compare to that of a stellar-mass black hole?

    35. Teaser
  35. What happens to the proper radial distance and the proper time at the Schwarzschild radius?

Updated 2021 Mar 5