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ASTR 3740 Relativity & Cosmology Spring 2017 Problem Set 4: Questions you posed.

  1. Using the expression for Hawking radiation from a Schwarzschild black hole, calculate the mass and radius of a black hole that could bring a kettle of water to the boil.
  2. Explain what you see and experience as you approach the central singularity of a Schwarzschild black hole.
  3. True/False: The horizon of a black hole is where photons can orbit in circular orbits, just skimming the surface without falling in.
  4. Classically, an outside observer sees a person falling into a black hole to freeze at the horizon, dimming and redshifting into the indefinite future. How does quantum mechanics change this picture?
  5. Do wormholes really exist? Explain.
  6. What do you see when you fall outward through the outer horizon of a white hole?
  7. If nothing can escape from a black hole, how can Hawking radiation escape?
  8. True/False: If you fall into a rotating or charged black hole, you will be vaporized at the inner horizon by enormously blue-shifted light.
  9. The horizon of a black hole is the boundary from which not even light can escape. Is the horizon completely black?
  10. As you fall into a black hole, the outside Universe appears distorted in what ways?
  11. When you fall into a black hole, the horizon appears to split into two. The horizon you fell through appears above your head, but there is another image of the horizon that remains below you. Did you actually fall through the horizon? Explain.
  12. Your friend proposes to you that you meet at the singularity of a Schwarzschild black hole, by fallig into the black hole starting at the same time and radius but at different angular positions. Explain why this might be problematic.
  13. You and a friend find yourselves spiralling towards the event horizon of a black hole. Not wishing to die alone, you rope yourselves together. Can you stay together after you have crossed the event horizon?
  14. You watch a friend fall into a black hole. You know that, in principle, the image of the friend will appear to freeze on the horizon for all eternity. Is that what you would actually see of your friend if you watched them through an optical telescope?
  15. How does the Hawking temoerature of a black hole change as the black hole gets smaller?
  16. A charged (Reissner-Norström) black hole has two horizons, an outer horizon and inner horizon. Why? The outer horizon is a point of no return. What happens at the inner horizon?
  17. You free-fall into a black hole along with a full-length mirror. What do you look like to yourself in the mirror?
  18. The exact mathematical solutions for ideal black holes contain white holes and wormholes. Do white holes and wormholes exist in reality?
  19. True/False: If you were able to survive the tidal force falling into a black hole, you would glimpse the singularity just before hitting it.
  20. Is there a big difference between falling into a Schwarzchild black hole (no charge or spin) versus falling into a charged or rotating black hole?
  21. If light is the fastest moving thing in our Universe, how come photons are not fast enough to escape a black hole?
  22. You and your friends inadvertently fall into a black hole while playing a game of soccer. What do you see of your friends and of the ball? How does the game end?
  23. What is a white hole? Could there be other universes connected to ours through a white hole?
  24. Classically, as seen by an outsider, the image of a probe that falls through the horizon of a black hole remains frozen on the horizon for ever. Is that what actually happens?
  25. Dropping out of warp speed on the Starship Enterprise, you find yourself at the event horizon of the supermassive black hole in the galaxy M87 at the center of the Virgo cluster. Oops. Can you teleport back out to your escape ship, the Millenium Falcon, orbiting outside the black hole?
  26. Is the temperature of the Cosmic Microwave Background (CMB) lower or higher than the Hawking temperature of a black hole in the Universe today? What is the condition for a black hole immersed in the CMB to evaporate? What does this imply about whether black holes are evaporating now or will evaporate in the future?
  27. True/False: A black hole is always cooler after Matthew McConaughey into it.
  28. A human is torn apart by the tidal force, the difference between the gravity between head and toe, as they fall to the singularity of a black hole. But is a particle, which has no size, also torn apart?
  29. Explain how gravitational lensing works.