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I always assumed the differing 'views' of what would happen crossing into a black hole was a product of the interplay of the equivalence principle and 'relativi

I always assumed the differing 'views' of what would happen crossing into a black hole was a product of the interplay of the equivalence principle and 'relativity of simultaneity' that Special/General relativity already accounts for. I had thought that upon reaching the event horizon the outside observer sees time 'stand still' because no light from your continued motion the other side of the event horizon can reach them, effectively freezing the observers view. Or thought of another way, the curvature of spacetime at the event horizon reaches the equivalent velocity of c due to the extreme warping of spacetime, so light can't escape and 'time' stops for the observers view of the freefaller because light can't get to them, the freefallers then image freezes and slowly fades. Special relativity says the relativity of simultaneity is pronounced at high % of c, would it not be pronounced in an extreme gravitation field? A gravitational field is equivalent to acceleration so... If the curvature of spacetime at the event horizon has an equivalent velocity inwards of c, thereby preventing light escaping, would this not lead the outside observer to see one thing and the freefallers to experience another which special relativity's relativity of simultaneity explains? I say this becaue the light cone escaping the black hole must experience high gravitational fields (i.e equivalence principle) and the free faller continues on their geodesic experienceing 'no' force (save for tidal forces which in the case of a large black hole won't spegetify them just yet). So the _outside_ observer is seeing the effect of the freefaller and the freefallers observable light cone experiencing the equivalence principle which necessarily would cause relativity of simultaneity to become more pronounced. At the event horizon, with an equivalent spacetime curtavure of velocity c, surely this would mean that the outside observer would see no more regardless of what the freefaller observs and all that would be accounted for by relativity of simultaneity. I guess I thought of it as applying relativity of simultaneity to a gravitational field (by way of the equivalence principle) and not just velocity as the train thought experiment did. Is this line of reasoning incorrect - I'm assuming it is - why?

Thrymr 11y ago
> Is this line of reasoning incorrect - I'm assuming it is - why? You're trying to reason about black holes with special relativity, rather than general relativity. Special relativity explicitly ignores acceleration (and equivalently, gravitation). You mention the equivalence principle, which is relevant, but "spacetime curtavure of velocity c" makes no sense, because the curvature leads to acceleration, not velocity directly.
- PuffinBlue 11y ago
  Well that was sort of the point really, I was seeing how special relativity's relativity of simultaneity would work in an accelerated reference frame from the point of view of both observers. Intuitively (dangerous I know) it seemed that just because you're accelerating, that doesn't mean relativity of simultaneity wouldn't apply. I assumed the equivalence principle would be relevant because thinking about simulaneity of relativity in an accelerated reference frame (like an accelerating train at high c) would mean any outcome of the thought experiment would likely be transferable to relativity of simultaneity in a gravitational field, seeing as path through curved spacetime and acceleration is 'equivalent' (with caveats). Spacetime curtavure of velocity c - this is clumsy language but c behaves differently right? It's a constant, so unlike a helicopter hovering above the earth, spacetime's curvature must 'equal' c at the event horizon i.e. cause it to travel on a curved path back towards the singularity, or at least cause it to orbit on the event horizon. In this sense I was thinking about spacetime itself as the thing that was accelerating and the light was stationary at the event horizon, which is just a mental analogue really and likely unhelpful.

Thrymr 11y ago

> Is this line of reasoning incorrect - I'm assuming it is - why? You're trying to reason about black holes with special relativity, rather than general relativity. Special relativity explicitly ignores acceleration (and equivalently, gravitation). You mention the equivalence principle, which is relevant, but "spacetime curtavure of velocity c" makes no sense, because the curvature leads to acceleration, not velocity directly.

PuffinBlue 11y ago
Well that was sort of the point really, I was seeing how special relativity's relativity of simultaneity would work in an accelerated reference frame from the point of view of both observers. Intuitively (dangerous I know) it seemed that just because you're accelerating, that doesn't mean relativity of simultaneity wouldn't apply. I assumed the equivalence principle would be relevant because thinking about simulaneity of relativity in an accelerated reference frame (like an accelerating train at high c) would mean any outcome of the thought experiment would likely be transferable to relativity of simultaneity in a gravitational field, seeing as path through curved spacetime and acceleration is 'equivalent' (with caveats). Spacetime curtavure of velocity c - this is clumsy language but c behaves differently right? It's a constant, so unlike a helicopter hovering above the earth, spacetime's curvature must 'equal' c at the event horizon i.e. cause it to travel on a curved path back towards the singularity, or at least cause it to orbit on the event horizon. In this sense I was thinking about spacetime itself as the thing that was accelerating and the light was stationary at the event horizon, which is just a mental analogue really and likely unhelpful.