There are a few coordinate systems to describe the inside of the BH:
Schwarzschild, behaves oddly inside the BH
Kruskal-Szekeres, space and time do not swap
Gullstrand-Painlevé, $t$ is the time measured on a clock held by an observer falling freely into the black hole
I have read a lot of questions and answers on this site about the interior of the black hole and spacetime there. There are very different descriptions, some say time and space swap, some say they do not, some say spacetime bends extremely, and basically that the only future is towards the singularity, $r$ becomes $t$.
It is not possible to list all questions. But none of them answers my question, since I am just looking for some clarification about the different statements in different answers.
where dannygoldstein says:
Once you've crossed the event horizon, all worldlines move backward in $r$. So we say that $r$ becomes timelike while $t$ becomes spacelike. But for $r<2GM$, the terms in the parenthesis are negative, so the time-spacelikeness of $dt$, $dr$ flip, and $dr$ becomes the only coordinate that contributes negatively to the metric line element. What this means physically is that you can only move forward in $r$, so in that sense $r$ becomes a timelike coordinate.
where Nanashi No Gombe says:
What you are missing is the observation that as you cross the event horizon, the lightcone gets so squashed that space and time swap their dimensions.
where John Rennie says:
Time and space don't swap places inside a black hole. The point of all this is that the coordinates are not spacetime - they are just labels we attach to spacetime.
These are very different descriptions and I would like some clarification on this. What exactly does swap and what does not in theory? The point of the question is only clarification, there is no other answer on this site that would answer my question because it is specifically, the amount of information and the different statements that are confusing.
- How exactly does spacetime change inside a black hole?