ASTR 3740 Relativity & Cosmology Spring 2023 Problem Set 3: Questions you posed.

1. 6 votes. As you fall into a black hole, outside observers see that last light from you slowly redshift as it “fights” the contraction of space. This contraction of space will thusly blueshift the light from the outside universe around the black hole. Blueshifted light by definition has more energy. If you fall into a black hole would you reach a point around the black hole where you are instantly incinerated by the high energy blueshifted light?
2. 4 votes. If Schwarzschild wormholes exist as solutions for Einstein's equations, why is it when a relativistic star collapse into a black hole, it doesn't produce a wormhole?
3. 10 votes. A crafty wizard is somehow able to build a perfectly elastic trampoline on the horizon of a black hole. You fall to the trampoline from a height l, do you ever return to a height of l from your perspective?
4. 8 votes. When all that's left in the universe is black holes and other dark and cool objects, will black hole explosions light up the night sky?
5. 10 votes. In a merger of two black holes, what would happen to you if you were directly between the two and were wearing an extremely strong space suit? What if you didn't?

Observations of black holes
6. Given that black holes trap light and cannot be seen, how have scientists been able to observe them?
7. Why can we treat an astronomical black hole by the assumption that it has no charge?
8. What are the characteristics of a Schwarzschild black hole?
9. What is the difference between a Schwarzschild radius of a black hole, and the radius of which an Einstein ring is made?
10. The energy released during accretion onto a black hole ultimately comes from thermonuclear reactions. True or False?
11. What does the “no-hair” state of a black hole refer to? Describe what is needed for a black hole to enter its “no-hair” state and why is it important?
12. How do black holes warp space and bend light of a star?
13. Where does the energy that black holes use to radiate Hawking radiation come from? What would happen if there was no mass left to accrete outside of the black hole?
14. Our sun will eventually go supernova and collapse into a black hole and when it does, the Earth will then be sucked into the black hole. True or False?
Near a black hole
15. If you and a friend traveled to a black hole and you stayed facing the black hole but your friend went around it and stopped directly behind it and shined a very bright light, what would you see?
16. The innermost circular orbit around a Schwarzschild black hole is a scalar multiple of the Schwarzschild radius. True or False?
17. Within the accretion disk of a black hole, we detect bright luminous matter. What causes this?
18. If we fired the probe directly upward from our spacecraft, the probe would escape to safety. True or False?
19. You are orbiting a supermassive black hole in a very advanced spaceship that can eject a large amount of its mass to change its trajectory. Since you and your spaceship can change your direction, unlike light, is it possible to dip into the event horizon and back out with sufficient speed and Δm?
20. If I placed a spaceman standing still on the ergosphere of a Kerr blackhole, what would change?
21. The Schwarzschild radius can be derived without general relativity using Planck mass and Planck momentum. Derive the Schwarzschild radius then calculate the radius for your mass.
22. Describe what it would be like, either yourself or light, to pass through the ergosphere of a Kerr black hole both in and against the direction of rotation.
23. Find and correct 3 errors in this statement: At 1 Schwarzschild radius from a black hole any circular orbit is stable, meaning any firing from thrusters would perturb the orbit greatly. At this distance you would be outside the accretion disk.
Frozen on the horizon
24. If everything that falls inside a black hole appears eternally frozen on its horizon, do they ever actually fall in?
25. Would a person appear to reach the event horizon of a black hole if they were moving at the speed of light? How could you tell?
26. Upon examining a black hole, you notice a flashlight in the exact center of the horizon that is pointed exactly vertically upward relative to the black hole's horizon. If the flashlight is turned on, when will the light reach you?
27. If I let a laser that emits green light every 2 minutes fall into a black hole, what will happen to the emitting light from my point of view?
28. How does an infalling astronaut appear to an astronaut outside the Schwarzschild radius and why?
29. From the point of view of an outside observer, someone falling into a black hole will appear to slow down, freeze, and then fade away. Why do they fade away and not just stay visible and frozen forever?
30. If you are an observer and watch your friend drift into a black hole, will your friend appear to be redshifted or blueshifted as his image freezes in time at the horizon?
Tidal forces
31. At what distance from a black hole of 30 solar masses would you be pulled apart (spaghettified)?
32. Would dipping into a stellar mass black hole, or dipping into a supermassive black hole be easier on the human body?
33. Let's say you launch yourself into a black hole with the goal of making it past the event horizon alive. How big should your black hole be? Does the size affect the forces you'd feel?
34. In which scenario would you have a better chance at survival (assuming you could withstand the crush of gravity and had a very good space suit on)? Passing by a 5 solar mass black hole, or a 3×10⁶ solar mass black hole? Why?
Inside the horizon
35. Is it possible to communicate with another person inside the horizon of a black hole?
36. Just before you hit the singularity of a Schwarzschild black hole, the presence of a single infalling photon is enough to induce tidal oscillations strong enough to tear you apart. True or False?
37. Space falls faster than light inside the event horizon of a black hole. If we go past the event horizon, will we experience time running backward and hence avoid hitting the singularity?
38. From the perspective of an observer falling into a realistic black hole, what changes falling past the outer event horizon as compared to the inner horizon?
39. If you were falling into a black hole and wanted to live to reach the other side, how would you survive, and would there still be a point of singularity in this case?
40. Does the motion in which someone falls into a black hole affect the traveler's perspective of what the black hole looks like as they approach the singularity? Think about angular momentum.
41. What is the singularity that we can see from both the Newtonian physics and the Schwarzschild geometry?
42. You have fallen into a Schwarzschild black hole and are currently at 0.9 Schwarzschild radii, and thus destined to hit the central singularity. Before you do so however, you look to the outside universe and see two observers; one orbiting the outside of the black hole and the other falling in after you. Whose clock runs slower from your point of view?
43. The Reissner-Nordström and Kerr-Newman solutions provide more physically plausible (vs. Schwarzschild) geometries for the inside of black holes, since they account for more properties of the black hole. True or False?
44. Explain how the equation for the Schwarzschild radius r_s shows that stationary frames do not exist for r < r_s.
45. By definition, black holes are objects so massive that their escape velocity exceeds that of the speed of light. Because of this, what relativistic effects would one experience during the journey to the event horizon of a black hole? Please describe in detail and also mention what an observer falling into the black hole would observe.
46. Assume that you have an indestructible and incompressible spacesuit and you jump into a black hole. Once you are within the black hole, you would be able to see the back of your head. True or False?

Updated 2023 Mar 3