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No I really just mean the plain and simple scenario. Imagine you knew nothing about escape velocity or black holes, then you would not be confused at all by the

No I really just mean the plain and simple scenario. Imagine you knew nothing about escape velocity or black holes, then you would not be confused at all by the idea that an object can move away from the Earth at any speed whatsoever, so long as its direction was away from the Earth. You don't need to move at Earth's escape velocity to move arbitrarily far away from the Earth. You could in principle travel all the way to the Andromeda galaxy without ever exceeding the Earth's escape velocity at any point. Now for some reason when people talk about black holes existing because the escape velocity exceeds the speed of light, then it tricks people into thinking things they would never have otherwise thought, like in order to move away from an object you need to be moving at that object's escape velocity. Like somehow if you don't move away from an object at its escape velocity then you can't move away from that object at all. Ignoring general relativity, if a black hole was nothing more than an object that had an escape velocity greater than the speed of light, then there's no reason why you couldn't enter the event horizon and then very slowly come back out, go back in, then sloooowly come back out, heck even come out and travel to an arbitrarily far galaxy and tell people about your adventure. Escape velocity does not mean being unable to move away from an object, not for Earth and not for a black hole either. Escape velocity just means the velocity where no further propulsion or acceleration is needed to continue moving away from an object. In general relativity, it's not simply that the escape velocity at the event horizon is equal to the speed of light, for if that were all there was to it, then simply bring some fuel with you to propel yourself away from the event horizon, feel free to do so at 1 cm an hour. In general relativity there are two perspectives, the perspective of the object entering the black hole where space-time curvature becomes so extreme that the spatial coordinate swaps places with the time coordinate in such a way that every future point is closer and closer to the singularity, and there is the perspective of an outside observer who sees an object getting closer to the event horizon undergo extreme time dilation and effectively freeze as their position perpetually smears itself across the entirety of the event horizon.

LorenPechtel 2y ago
But you need some sort of propulsion system if you wish to escape while moving slower than local escape velocity. Rockets can do it because they have such a propulsion system. (Although in practice any ordinary rocket will normally exceed the escape velocity from the surface of the Earth. Due to Oberth you want to do your burn as close to the planet as possible and escape velocity from low orbit is only slightly less than from the surface. Since when you head out into interplanetary space you're normally going somewhere you're carrying extra velocity.) Light has no propulsion system, it doesn't make it out if the local escape velocity exceeds lightspeed even if there was no event horizon or other space warping effects involved.
- Maxatar 2y ago
  Make it out of what though? If all there is to consider is escape velocity, than light, or any object whatsoever, can absolutely escape the event horizon if it's moving at anything remotely close to the speed of light. Without propulsion it won't be able to travel to an arbitrarily far distance, but it can certainly escape the event horizon in any scenario other than if its initial velocity came from when the the object was at the center of mass. You wouldn't even need a very significant velocity to escape the event horizon of a black hole if you had that velocity within a region close to the event horizon. As I said, escape velocity is a good way to motivate the idea of a black hole, it serves a pedagogical purpose, but the story doesn't stop there and you quickly realize that in fact, the escape velocity itself has little to do with black holes. It just happens to share the same underlying principle that the calculation for the event horizon has.
  - LorenPechtel 2y ago
    And note that he was looking at that--light might come up but not get away. The model is different but the results would look the same to an outside observer.

LorenPechtel 2y ago

But you need some sort of propulsion system if you wish to escape while moving slower than local escape velocity. Rockets can do it because they have such a propulsion system. (Although in practice any ordinary rocket will normally exceed the escape velocity from the surface of the Earth. Due to Oberth you want to do your burn as close to the planet as possible and escape velocity from low orbit is only slightly less than from the surface. Since when you head out into interplanetary space you're normally going somewhere you're carrying extra velocity.) Light has no propulsion system, it doesn't make it out if the local escape velocity exceeds lightspeed even if there was no event horizon or other space warping effects involved.

Maxatar 2y ago
Make it out of what though? If all there is to consider is escape velocity, than light, or any object whatsoever, can absolutely escape the event horizon if it's moving at anything remotely close to the speed of light. Without propulsion it won't be able to travel to an arbitrarily far distance, but it can certainly escape the event horizon in any scenario other than if its initial velocity came from when the the object was at the center of mass. You wouldn't even need a very significant velocity to escape the event horizon of a black hole if you had that velocity within a region close to the event horizon. As I said, escape velocity is a good way to motivate the idea of a black hole, it serves a pedagogical purpose, but the story doesn't stop there and you quickly realize that in fact, the escape velocity itself has little to do with black holes. It just happens to share the same underlying principle that the calculation for the event horizon has.
- LorenPechtel 2y ago
  And note that he was looking at that--light might come up but not get away. The model is different but the results would look the same to an outside observer.