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ASTR 3740 Relativity & Cosmology Spring 2020 Problem Set 3: Questions you posed.

  1. What happens to time when you approach a black hole?
  2. An observer watching someone falling into a black hole sees them slow down and redshift until they completely stop at the event horizon. What does the falling person see when they look back at the observer?
  3. Suppose you have managed to stay suspended at (just above) the event horizon of a black hole, but it is about to merge with a second black hole. At the instant that the two black holes event horizons merge, what would you as the observer experience?
  4. The complete Schwarzschild geometry consists of a black hole and a white hole. A white hole is a black hole running backwards in time: whereas in a black hole space falls inward faster than light, in a white hole space goes outward faster than the speed of light. Wormholes join the positive square root solution and the negative square root solution of the Schwarzschild metric. Are wormholes feasible in reality?
  5. You and a friend are unfortunately falling toward a black hole at the same time, though at different locations in longitude and latitude. As you both continue to approach the singularity, will you ever meet? Why or why not?
    Wormholes
  1. The space around a black hole with no charge or angular momentum is often represented as a waterfall of space which passed the event horizon flows faster than the speed of light. Wormholes are similar to these spacetime waterfalls, except there can be outward flow of space and time due to change. What property of nature keeps material from riding this reverse waterfall out of the black hole? Why?
  2. In the Penrose diagram of a black hole, there maintains a fictional symmetry where for every black hole there is an adjoining white hole (as well as a symmetric parallel universe). How might we go about understanding a white hole, and why does it make sense to theorize them as existing?
  3. What are some similarities and differences of falling into a blackhole vs. falling through a wormhole? Why can't you fall through a wormhole successfully?
  4. What evidence is there for the existence of Schwarzschild wormholes? If one appeared, what would happen to it inside the black hole?
  5. If someone from another universe enters a wormhole from their side at the same time I enter the wormhole from the other side, do we meet at the same time or does it depend on our masses? What if someone enters after us?
  6. Can a wormhole really exist?
  7. Why is it impossible to pass through a wormhole?

    8. Outside the horizon
  8. What are relativistic jets? How are they produced, and are there specific circumstances that must be met for their production to occur?
  9. What three quantities describe a black hole with no hair?
  10. What radius would the Sun have to be to collapse into a black hole? What is the name of this radius?
  11. What does a bright object eclipsed by a black hole look like to someone looking at the black hole?
  12. You travel through the Milky Way galaxy in your futuristic spaceship. Out of nowhere you realize your ship is being pulled in another direction than you are heading. You then realize you are heading for a stellar mass black hole. Neglecting the tidal forces, will you fall directly through the event horizon? Supermassive black holes may allow interstellar travelers to go in with unnoticeable tidal force, thus posing a threat to them. Is this true? I read it once. What would the tidal force at the event horizon of SGR A would be like? Would it be noticeable?
  13. You are squaring off with your nemesis and have one shot with your newly developed teleport gun that sends whatever it hits hurtling towards a black hole at near the speed of light. Your goal is to never see your nemesis again, what do you do? Assume you have infinitely powerful eyes that allow you to see anywhere in the Universe, also assume both you and your nemesis are fully immortal and invulnerable.
  14. What is the closest possible circular orbit around a black hole, in terms of Schwarzschild radii. Is this orbit stable or unstable? Why is this the closest circular orbit that can be maintained?
  15. Suppose that you look at the event horizon of a black hole from some arbitrary observation point outside of the event horizon. How much of the event horizon would you be able to see, and why?
  16. Many media describe black holes as having gravity so strong that not even light can escape from them, but this notion is misleading. How it is misleading? Describe why the actual explanation is consistent with the main postulate of special relativity, that nothing can go faster than the speed of light.

    17. Through the horizon
  17. You are falling into a black hole. Right when you get to the horizon at the black hole, you emit a photon vertically upward. How does the photon move?
  18. Explain what you as an observer outside the black hole sees when your friend passes the horizon, at 1 Schwarzschild radius.
  19. You are hovering above a black hole at a safe distance with multiple synchronized clocks. You launch each clock into a stable orbit around the blackhole, but keep one on your ship as you travel down towards the black hole. Once inside the event horizon, how do the clocks you deployed appear to differ from your clock?
  20. You as an outside observer watch person A falling into a black hole. Just before A falls through the horizon, A turns on a flashlight and points it at you, then turns it off. After that, A passes the horizon. You, the outside observer, see A freeze at the horizon, so will you see the flash sent out by A? If yes, how long would it last?
  21. Why is there no turning back past the Schwarzschild radius of a black hole?
  22. In the video of falling into a Reissner-Nordström black hole, when entering the black hole, the visible light from the original universe takes up most of the sky (solid angle), while when exiting the white hole, the visible light from the new universe only starts off taking a small portion of the sky. Why is there this discrepancy, despite the conditions when crossing event horizons being relatively similar, though in opposite directions?
  23. How many licks (?) does it take to get to the center of a black hole?

    24. Hawking radiation
  24. If black holes are black, then shouldn't that mean that if we take a blackbody spectrum of it that it would just be zero across the board? Why or why not?
  25. What is the black hole information paradox? Do black holes violate conservation of information?

    26. True or False?
  26. A light source behind a black hole always appears as two images (one exactly opposite the other).
  27. At 1.5 Schwarzschild radii, it is possible to maintain a stable circular orbit.
  28. If you fall into a very massive black hole, you'll be torn apart faster than if you fell into a less massive black hole?
  29. At the Schwarzschild radius, solid spherical angles appear to be infinity due to perceived length becoming infinitely large.
  30. As a black hole increases in size, its Hawking tempreature increases proportionally to the black hole Schwarzschild radius?
  31. The fact that black holes violate the second law of thermodynamics is the reason we do not yet understand what happens to space and time at the singularity of a black hole.
  32. If there are 2 universes connected via the wormhole in between them, and this is the case for all other black holes in our universe, then universes would have to overlap and create more universes through the new wormholes, creating infinitely many universes.
  33. Yes or no? During your lifetime, is it realistic that an explosion due to a mini black hole evaporating under Hawking radiation could be spotted on Earth?

Updated 2020 Feb 24