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ASTR 3740 Relativity & Cosmology Spring 2014 Problem Set 4: Questions you posed.

1. True/False: There exists an orbit around a black hole such that a craft can travel backwards in time.
2. If you were orbiting a black hole and wanted to send a tachyon into the black hole, what direction would you need to send it?
3. True/False: If you are flying in a space ship around a black hole, the last stable orbit you can descend to is 1.5 Schwarzschild radii.
4. True/False: Black holes are like vacuums that suck in matter, so there is no way to orbit one.
5. Can anything move faster than the speed of light?
6. True/False: The location of the innermost unstable circular orbit is at 1.5 Schwarzschild radii from the singularity. In order to maintain a circular orbit the velocity must equal the speed of light. The area covered at this radius is also sometimes referred to as the Schwarzschild surface.
7. Inside a black hole, space falls faster than the speed of light. Explain why this does not violate Einstein's law that the speed of light is the universal "speed limit".
8. Suppose you drop two probes into black holes of mass M and 2M and observe their redshifting images on the horizon. Quantum mechanically, which image would disappear first?
9. Your mission, if you choose to accept it, is to document the experience of diving into a black hole. Assuming you had the technology to survive and return back home, what would you include in your report when descending from one Schwarzschild radius?
10. True/False: You can see Einstein rings of objects directly behind a black hole up until you pass through the horizon.
11. How is it that we are still able to observe objects falling into a black hole even after they pass into the black hole where gravity is so strong that not even light can escape it?
12. What causes a singularity to exist?
13. True/False: Once inside the Schwarzschild radius as we are falling toward the singularity, space seems to distort around us so that we see both inside the black hole and outside at the same time.
14. Ignoring the effects of tidal forces, if you were at the center of a spherical mirror of a diameter about 3 times your height, what would the scene look like as you approach/enter a black hole?
15. We somehow got stuck in a circular unstable orbit and have lost all rocket power so escape and demise are both impossible - we are stuck in a perpetual orbit around the black hole! Alas, we still have a single probe we can send out to call for help. Which direction must we send the probe in order to save ourselves?
16. Abandoning the classical notion that black holes are completely black and ignoring infinite redshifting of any image at the horizon, argue why you would actually observe said image to disappear in a finite time.
17. Why can you not survive falling into a black hole?
18. If you had the unlucky (or lucky?) experience of falling into a black hole, would your body be intact? Why or why not, and what would be your experience if you remained intact?
19. If the sun were suddenly replaced with a 1 solar mass black hole, what would happen to the orbit of the Earth?
20. True/False: Once you are in an unstable circular orbit around a black hole (3 to 1.5 Schwarzschild radii), there is no chance of changing your orbit to escape safely.
21. What is the difference between a charge-less black hole and a charged black hole? Which would be more likely to exist?
22. Will a photon emitted inside the event horizon of a black hole reach the event horizon and then fall back in, will it start moving up until the inward momentum cancels the outward momentum of the photon, or will it simply fall further into the black hole regardless of the direction in which it was emitted? Why?
23. Could a black hole be used as a time machine? How so? Could the time travelers go only forward, only backward, or go in both directions in time?
24. You are planning an intergalactic "road trip" in your brand new spaceship with your friends. What kind of research must you do before you hit the intergalactic highway? (Hint: You don't want to run into black holes, so you would you find them in order to avoid them?)
25. If a black hole is accreting, at what distance would the closest matter of the disk be in stable orbit around the black hole?
26. If the gravitational strength of a black hole is so strong that not even light can escape, why do some black holes emit jets?
27. If you are in an orbit at the Schwarzschild radius (moving at c) and you shoot a laser directly opposite your direction of travel, what happens?
28. When an object is directly behind a black hole, why do we observe an Einstein ring?
29. A star sits directly behind a black hole from your line of sight. Can you see the star? If so, what does it look like?
30. True/False: NOTHING can move faster than light.
31. True/False: When you pass through the event horizon of a black hole, all the light that has been trapped inside becomes visible to you and it is extremely bright.