ASTR 3740 Problem Set 3: Questions you posed

3 votes. In the twin paradox, what happens to the proper times of you and your twin if there is a black hole along the line of sight between you?
9 votes. NASA is looking for volunteers to be the first human to travel into the depths of a black hole. Given your silly thirst for adventure, you're the first to volunteer. Which black hole do you choose to journey into, a stellar black hole (ten solar masses), or a supermassive black hole (a million solar masses)?
6 votes. On a spaceship a safe distance from a non-rotating black hole, you synchronize two clocks, and lower one close to the black hole before pulling it back to the ship. Are the clocks still synchronized?
2 votes. Can a black hole destroy itself by sucking itself in?
1 votes. Is it true that if you fall into a wormhole you will be forced through a singularity at the center and be spit out the other side, leaving you disintegrated in another universe?

Near a black hole

Why can't you tell when you pass through the event horizon?
Given that mass falling on to a black hole appears to freeze at the horizon and never fall in, how can a black hole gain more mass and grow?
Is it true that any light behind the horizon of a black hole will be trapped inside?
From the point of view of a distant observer, does the clock on a person orbiting a black hole appear to run slow or fast?
You want to park your black hole research station on a stable circular orbit, but as close to the black hole as possible. What is the smallest possible stable circular orbit?
You sit at radius 1.5 Schwarzschild radii from a Schwarzschild black hole. What is special about this position?
If you are near a black hole but outside its horizon, can you see the back of your own head?
An outside observer watching a person orbit a black hole would see then blueshifted as the orbiter come towards them, redshifted as they move away. Does the orbiter themself experience time go by steadily?
From a safe distance you talk via a direct-line cell phone with your friend falling into a black hole. What happens?
You watch the eclipse of a planet by a large black hole. What do you see?
How do tidal forces from a black hole's gravity distort an image?
What would your friend see if they watch you fall into a black hole?
How do emitted photons in a gravitational potential well appear to an observer at rest outside the potential?

Charged black holes

You somehow fall into a Reissner-Nordströt;m wormhole. At what point on your journey do you first see light from the “new” universe that you encounter?
What is the difference between a Schwarzschild black hole and a Reissner-Nordström black hole? How would a journey into or through them be different?
What are the mathematical differences between a Schwarzschild black hole and a Reissner-Nordström black hole?
What happens if a black hole has charge?

Wormholes

If we fell into a Schwarzschild wormhole and caught a glimpse of the alternate universe that it connects to, would we be able to tell our friends back home of the amazing view?
The complete Schwarzschild geometry includes a black hole, a white hole, and a wormhole connecting two separate Universes. Explain why visiting the other Universe would be impossible.
What would you see if you passed through a wormhole?

No-hair theorem

What does the no-hair theorem state?
The no-hair theorem states that the geometry outside the horizon of an isolated black hole is characterized by what three quantities?
What does it mean to say that a black hole has “no hair”?

Hawking radiation

Where does the energy come from that a black hole at rest radiates in Hawking radiation?
What is the lifespan of a 10 solar mass black hole which loses mass to Hawking radiation?
If a 20 solar mass black hole absorbs a 5 solar mass star, how does its Hawking luminosity change?
Of two black holes A and B, A has radius 16 times larger than B but temperature half that of B. Which black hole is more luminous?

Updated 2022 Mar 7