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This is not a duplicate, I am not asking about any kind of time dilation caused by a BH. My question is about the direction of time (and if it is possible to have different directions for time, other then back and forth) inside the BH and not its relative speed.

I have read this question:

Time in our Universe versus time in Black Holes

Where Safesphere in a comment says:

The idea of a black hole being a shell just outside the horizon is well known. However your personal theory of the shell being inside the horizon has nothing to do with physics, but is based on a lack of knowledge or understanding of the Schwarzschild metric. Time inside a black hole doesn't move slower relative to the universe. Instead, time inside a black hole moves in a different direction and for this reason can't be put in any reference at all to the time elsewhere in the universe, not "slower", not "faster", nothing. You can't race to the destination while moving in different directions.

This is a gamechanger. I thought that time's is a one dimensional, single direction phenomenon, that is universal for our universe, and it goes in the same direction everywhere in the universe.

But this comment would mean that there is a part inside our universe (yes if we consider the inside of a BH part of our universe, at least in 3D it is since it is just the inside of a shell), that has a direction for the time dimension that is different from the other parts of the universe.

So this means that time goes in a different direction inside the BH then outside of it. Which direction does it go? I thought that time was just a single dimension, and there are only two ways to go, and going back in time is just a theoretical phenomenon, not actual physics.

But the idea that time goes in a different (not even backwards), but in a completely different direction (like perpendicular direction) is something that is completely hard to imagine without more dimensions.

Question:

  1. Is it true, does time go in a different direction inside the BH, then outside of it?

  2. How is this possible, does time not flow in the same direction everywhere in the universe, and is time not a single dimension, where there are only two ways, back and forth?

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  • $\begingroup$ "So this means that time goes in a different direction inside the BH then outside of it. Which direction does it go?" - In our view from outside, time inside the horizon goes toward the center of the black hole and ends there. $\endgroup$
    – safesphere
    May 22, 2019 at 5:17
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    $\begingroup$ (1) How would you propose to compare "directions" at two different points in curved spacetime? (2) Given that each causal worldline has its own proper time ("twin paradox"), what do you mean by "the direction" of time? Are you asking why/when it's possible to have a globally consistent distinction between future and past? We usually only consider time-orientable spacetimes, which by definition means that such a consistent distinction is possible. $\endgroup$
    – Chiral Anomaly
    May 23, 2019 at 13:47

3 Answers 3

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In a general way, for fundamental questions about time you must refer to proper time, not to coordinate time. Time in the form of proper time is the aging/ the duration of particles. There is no "direction" for such aging.

Concerning the Schwarzschild metric of a black hole it is said sometimes that time and space are "interchanged" within a black hole, but such an internal metric of black holes has two issues:

1.According to the principle of cosmic censorship, we do not know what is happening inside a black hole. And so it is going in this sense that Schwarzschild metric is providing weird results for this case.

2.Historically, the assertion that time is "changing direction" is an extrapolation of the external metric that was done without defining what it means that "time is going in another direction". However, as long as nobody has defined such thing, it may not be considered as a solution of the Schwarzschild metric. Or the other way around: Due to cosmic censorship, there is no defined time evolution inside a black hole.

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  • $\begingroup$ It isn't the Schwarzschild metric that produces weird results, it is Schwarzschild coordinates, which are of limited use at $r<r_s$. Other coordinate systems are better behaved. $\endgroup$
    – ProfRob
    May 10 at 23:04
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In GR, space-time is a single entity known as a manifold.

In the geometrical model, one actually thinks of 'direction' as being in a distinct space (the 'tangent space') at every point in space time.

By 'direction of time', I'll take that to mean the forward light cone, or part of the tangent space that is time-like.

There is a relationship between the tangent spaces, which in GR can be determined by the metric, but gravity is intimately tied to the fact the relationship is non-trivial.

What this means is that there is no single 'direction of time' because the space in which direction is defined itself varies throughout the universe.

In GR it is often difficult to distinguish what is really intrinsic and what is an effect of coordinates.

In the Schwarzschild hole, we find that the $r$, $t$ coordinates misbehave at the event horizon and that once inside $r$ itself becomes more like a time coordinate and heads to zero. Coordinate system changes are used to get a better grasp of the horizon.

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If time represents all change in the current state of the universe, then any change in the relationship of variables in spacetime could be interpreted as a change in the direction of time. Example - lightspeed is no longer C in all frames of reference.

Apologies in advance for this short, uninformed answer.

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