It's #BlackHoleFriday! So today, I'm going to tell you about how using a black hole could help us reach one of humanity's greatest aspirations that's only ever seen in sci-fi movies and TV shows: time travel! (Well, *kinda*) A thread:
(GIF credit: jila.colorado.edu/~ajsh/insidebh…)
(GIF credit: jila.colorado.edu/~ajsh/insidebh…)
Special Relativity tells us that, for objects that move really fast (like a spaceship), or ones in a large gravitational field (near a star, or say, a black hole), time moves slower than for objects at rest (for example, on Earth).
And I'm here to tell you that, if you took a spaceship and circled around a black hole, time would move slower for you than, say, your friend back on Earth! We'll calculate a specific example, and factor in the time it takes (and what happens to it!) for a spaceship to get there!
Now, back to how time is distorted by things moving fast, or objects near large masses: While it seems weird, let's think about it: the theory of relativity tells us that space and time form a "fabric" we call spacetime; that is to say, time and space are sort of woven together.
This matters, because then, traveling at a distance could cause time to move differently than if you're stationary---IF your movement is close to the speed of light, or near a body that's so massive it warps spacetime a lot.
Now, light speed: no matter where you are, light speed (in vacuum) is *always* the same: 3*10^8 m/s. This is true on Earth, and on a spaceship. What changes for each observer is the frequency of light: it could be redshifted, or blueshifted, for an outside observer.
Here's where stuff gets interesting: let's make a "light clock", where we have a mirror at each end separated by a distance of 3*10^8 meters. Then, if we shoot a beam of light from one end, it'll take one second to get to the opposite end, and a second to come back.
Now, take this light clock on a spaceship traveling near light speed (call it c): holding the clock upright, we shoot a beam of light up. We're also *moving* through space close to c, so the light beam kinda needs to travel a bit more, or *longer*, to get to the other end.
Bc it takes the light beam longer to get to the opposite mirror on the spaceship, it takes longer for 1s to pass---time moves *slower* for the person on the spaceship. Here's a gif of a light clock on Earth, and one on a spaceship. (Cred: John D Norton, UPitt)
Similarly, when light travels around a black hole, it travels around spacetime that's curved due to the black hole. This causes its trajectory to bend, which also means it takes longer to get around it. So around a black hole, time moves slower than it does for a person on Earth!
Alright, equipped with that, let's say you and your friend decide to do an experiment together. You get a ship that travels at 95% the speed of light c, and you'll travel to a black hole that's 20 times the mass of the Sun and takes 10 years to get there (as measured on Earth).
First we'll find how much time passes for you on the spaceship. We'll use the equation in the picture (from Wikipedia), and solve for Δt to find the time that passes for you, and Δt' is your friend's time on Earth, which 10 years. The velocity v is 95% light speed, so 0.95 c. 
Plug that in and you'll get that 3 years pass for you, while 10 pass for your friend on Earth.
We're at the black hole! To be safe, we'll keep ourselves 1.5 times the Schwarzchild radius (event horizon) above the black hole. This is the closest we can get to a black hole and remain in stable circular orbit. Any closer and we'd need fuel, but we wanna save that to go home.
Now we'll use the equation in the picture (Wikipedia) to find how much time passes for you if you stay in orbit for a time that's 10 years for your friend on Earth. Here, t_f is your friend's time. Let's find r_s (the Schwarzchild radius) for the 20 solar mass black hole.
Plugging in the gravitational constant G, speed of light c, and the mass, we get 59 km for the Schwarzchild radius. We'll stay 1.5 times above that, here. Plugging that in, we find that about 6 years pass for you, while 10 passed for your friend.
If we wanted to use fuel to make sure we don't get sucked into the black hole and get closer, the time that passes for us would be significantly less! Eg: if we wanted to be 3 km above the Schwarzchild radius (so 62 km), we'd find only 2 years pass for us! But we're being safe.
Now, we go back home, which is the same as the time it took to get to the black hole: 10 years for your friend, 3 years for you. Then: your friend has aged 30 years, while you've aged 12!
Notice the following: we need to get into orbit around the black hole, but it doesn't really matter what our speed is, it's all about the gravity! This of course would cause us to move super fast. While time dilation in a spaceship requires us to move *really fast*.
And the takeaway is: black holes warp the fabric of spacetime so much it causes time to move slower for us in the spaceship around the black hole! Black holes are weird and amazing things.
Ooof that thread took long to write!
