# I Is time bidirectional in a black hole?

#### mousheng xu

I just watched a youtube video saying that somewhere in a blackhole, time is bidirectional (can go to the future and can go to the passed), but space is one-directional.

Any introduction material on this subject?

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#### PeterDonis

Mentor
I just watched a youtube video
YouTube is not a good source for learning science.

somewhere in a blackhole, time is bidirectional (can go to the future and can go to the passed), but space is one-directional.
This is not correct. Which is a good illustration of why YouTube is not a good source for learning science.

Any introduction material on this subject?
There are plenty of good textbooks on General Relativity out there. Sean Carroll's lecture notes on GR are online and covers the basics of black holes:

#### PeterDonis

Mentor
Moderator's note: Thread moved to relativity forum.

#### Ibix

I just watched a youtube video saying that somewhere in a blackhole, time is bidirectional (can go to the future and can go to the passed), but space is one-directional.
If you write down the metric (the mathematical object describing the "shape" of spacetime) outside a black hole using Schwarzschild coordinates, and repeat the exercise inside, you find that they look the same. It's natural enough to use the same coordinate label inside and outside since the maths looks the same. But it turns out if you do that then outside you are using the letter $t$ to describe your position in time and the letter $r$ to describe your position in space, but inside the hole you are using $t$ to describe your position in space and $r$ to describe your position in time.

The important thing to realise is: just because I label something $t$ does not mean it's actually time. The universe does not care what letters I use. Your YouTuber has not realised this (or has chosen to ignore it for coolness factor).

So yes, inside the black hole I can freely increase or decrease my $t$ coordinate, but my $r$ coordinate always increases. But this is because I'm using $t$ to describe my place in space and $r$ to describe my place in time, not because I'm free to travel backwards in time.

An analogy to this can be made on the surface of the Earth. Face north. Now north is forwards, south is backwards, east is right and west is left. Take a step forward. Same thing - north is forwards, etc. Keep stepping forwards. Eventually you reach the north pole, where every direction is south. One more step and the pole is behind you - so suddenly north is backwards, south is forwards, east is left and west is right. You can now take to YouTube and make videos about how it's impossible to move forward at the north pole (because north is forward and every direction is south) and that forward and backward change meaning when you go through the north pole! Or you can just realise that north doesn't always mean forwards.

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"Is time bidirectional in a black hole?"

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