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by pa7x1 2079 days ago
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.

2 comments

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.