Ok that explains how space becomes timelike. But I never hear anyone address how time becomes spacelike. In what sense does it become spacelike? Can one move back and forth in time inside the event horizon?

The radial direction of the inside of the Schwarzschild Black Hole is timelike. This means that; inside the event horizon, the inevitable passage of time becomes the inevitable move towards the singularity at the center of the Black Hole.

To answer your question in clear terms: No, you cannot move freely in the radial direction. Only towards the center, in the same way you cannot move freely forward or backwards in time.

You paraphrased the GP post about space becoming time, but didn't answer the Parent question about time becoming space:

> In what sense does [time] become spacelike? Can one move back and forth in time inside the event horizon?

Sorry, I missed that. The time direction does indeed become spacelike inside the black hole. The most remarkable consequence of this is that the singularity is at the future of every test particle that crosses the horizon.

This can be seen best in a conformal diagram or Penrose diagram (now that he has a Nobel prize might as well use the name of his creator).

Here is the Penrose diagram of a star collapsing gravitationally into a Black Hole and its evaporation via Hawking radiation: https://fias.uni-frankfurt.de/~hossi/Bilder/BR/bhevap_l.jpg

You should track the r=0 line, initially it points upwards (it's timelike) as it chugs along at the center of the star as it collapses gravitationally. When the BH forms, it becomes horizontal (spacelike) and lies at the future of every test particle that enters into the BH. The singularity is inevitable for anything that crosses the horizon.

The Black Hole will at some point have radiated all its energy in Hawking radiation at which point it disappears and r=0 becomes timelike again.

Unfortunately it's hard to make it easier to understand without indulging in some math.

Considering a point particle, what constrains it from orbiting [which is what I'm assuming we're meaning here as all matter has to move radially to cross the event horizon]? If it had a tangential component to its momentum prior to meeting the event horizon (EH) wouldn't it continue to orbit past the EH?

Nothing forbids a slight tangential component but the movement of the test particle is inevitably decreasing in r.

Closed orbits are impossible though, all test particles finish at the singularity in a finite amount of proper time.

I think by definition the event horizon can only be crossed in one direction (towards the center). By this I mean nothing escapes once it is past that point. It's defined by being the point of no return

It is the point at which nothing, no matter how fast or massive, can possibly return from the gravitational pull. For instance: light, traveling at the speed of light in a vacuum, cannot escape once it has crossed the event horizon; it's pulled inevitably inward.

> what constrains it from orbiting

Not quite what you seem to be asking, but the event horizon is the point where[0] the escape velocity is equal to the speed of light; the orbital velocity at that distance is greater (by a factor of ln 2 IIRC, so v_orbital ≈ 1.44c). There's a more distant distance, called the innermost stable orbit or the photon sphere, where the orbital velocity is equal to c (so photons will orbit if you emit them tangentially at this height), but the escape velocity is only ~0.69c.

0: It's not quite right to say that that's because the escape velocity is equal to c, though.

It just becomes like space. You can freely move around it without any issues. It’s no longer time, just as the radial direction is no longer space.

How it happens? Normal spacial direction has positive sign. Time has negative. When crossing the horizon the equations become such that t gets a positive sign and the radial direction a negative one. After that they behave as expected.

This reminds me of the games you can play flipping signs in relativistic equations when you make v > c. You can interpret those in a lot of fun ways too.

Is that because you could move away from the center (a bit) to delay your progress toward the center singular?

You can’t move away from the center. You can move in direction around it (while still moving towards it at the same time). And you can move in the previously time now just space.

Delaying your fall is precisely the same as trying to avoid tomorrow by moving around. Moving away from the center is like moving back in time. No matter how you move in the spatial dimensions you can’t do it.

With the exception of faster than light travel. That allows you to move away from the center, and it also allows you to avoid tomorrow. It’s pretty much the same as time traveling in general relativity.

To be fair, the universe will never confront you to such a puzzling situation, as it will kindly squash you under heavy gravity before you come close to any object so massive.

Not necessarily, a supermassive black hole can have quite bearable gravity at the event horizon (as the event horizon radius depends linearly on the mass and the gravity declines quadratically with distance). You still wouldn't be able to communicate your experiences though.

What is supposed to happen with different types of chemical bonds? If half of a molecule is inside a black hole and half is outside, the half inside is necessarily constrained to the black hole, while a molecule outside does not have such constraint. The chemical bonds should be also necessarily broken at least for a moment, since an atom inside black hole can not exert electromagnetic effects on an atom outside black hole. Wouldn't it create a bias across your whole body with some really weird atomic / chemical consequences?

Nothing happens (locally) at the event horizon, everything works as normal. The analogy that is often used is fish upstream from a waterfall. At some point the current of the stream becomes so strong that the fish can no longer escape from the waterfall, but actually at that point nothing happens from the point of view of the fish, since it is carried by the current, you need a global view to notice that the fish is doomed past that point.

And similar in case of a black hole, you are falling through the event horizon and nothing happens, it is just that calculating what you need to do to escape, you note that it is too late.

To expand a bit on the molecule situation, when one of the atoms is inside the black hole, then parts of its electric field are still outside and influence the other atom. To have the other atom escape to infinity, you would need to break the part of the bond "still outside" and the gravity of the black hole.

> If half of a molecule is inside a black hole and half is outside,

You know how the universe is expanding, such that the milky way is moving away from (sufficiently) distant galaxies faster than the speed of light? But chemistry still works fine here? When you fall into a black hole, you accelerate until you're moving away from the rest of the universe faster than light, but all your atoms are still (relatively, assuming the black hole is large enough to have negligible tidal forces) stationary relative to each other. The event horizon is just the point where your speed relative to the effectively-distant[0] outside universe exceeds the speed of light. Any signal you emit can't be moving facter than c relative to you, so it will always be moving away from the outside universe (v<-c implies v+v'<0).

0: "Nothing can move facter than c" refers to relative motion of objects near each other, which is why the Hubble expansion of the universe doesn't contradict that either.

In General Relativity, locally all reference frames are flat. This does not change at the event horizon, chemistry continues to work normally. It is just that in the time it takes for half the molecule to affect the other half, the other half will have slipped across the event horizon.

There is a classic analogy of light traveling through space-time being like ants crawling on a balloon. A black hole is a spot where the balloon is being sucked in. Faster and faster as you get closer. The event horizon is where the speed at which the balloon moves matches the speed of the ant. There is nothing special from the ant's immediate perception about this line, but if the ant crosses, it is doomed.

Doesn't an event horizon imply a gravitational pull so strong not even light can escape? Isn't the effect of gravity the same at the event horizon for all sizes of a black hole?

I thought the size only affected the "acceleration" of the gravitational pull based on the distance from the singularity? A supermassive black hole means you will take longer to be spaghettified, but it will still happen and it will happen before you cross the horizon, won't it?

In some sense, there is no such thing as a gravitational pull. What there is is a curvature of space-time that causes an apparent force in some coordinate systems [0]. For a sufficiently large black hole, gravity is effectively constant in the vicinity of the event horizon; which means there exists a coordinate system where the space around (a small region of) the event horizon is essentially flat space. From the perspective of an outside observer, you would appear to flatten as you approach the event horizon, but this is a consequence of the coordinate system. You don't feel any effect at that point.

The reason light cannot escape from past the event horizon is that that is the point where space-time is so warped that what you consider a perfectly normal time axis is, from the perspective of an outside observer, now pointing in a spatial dimension directly towards the center of the black hole.

In contrast, regardless of how small you are, there is some point where you do experience tidal forces and feel yourself getting spaghetti. For a small black hole, this is before you pass the horizon, for a large black hole, it is after.

[0] The distinguishing feature between a real force like gravity, and a truly fictitious force like the centrifugal force, is that for the later, you can construct a coordinate system where the force disappears at all locations. For a real force, you can construct a coordinate system where the force goes away at any given point; but there will always be some point with an apparent force.

A uniform force doesn't do anything harmful to you. You get stretched into spaghetti by the difference in force between the ends of your body. In large black holes that difference can be small even as you pass through the horizon (where the total force is large).

I have heard of space becoming timelike, but have never heard of time becoming spacelike in a black hole. Do you have more information on that?

PBS Space Time is pretty decent and understandable source if one doesn’t want to wade trough the maths. I heavily recommend the whole black holes playlist. https://www.youtube.com/playlist?list=PLsPUh22kYmNBl4h0i4mI5...

I do want to wade through the maths, and I have to some degree, and I've never come across time becoming spacelike (which would imply rotation past the null vector, which afaik is not something that happens in a black hole).

Thanks, that's much more helpful, although still pretty mind-bending.