Comment by Jerrrrrrry

Comment by Jerrrrrrry 10 months ago

  >space cone

  >light cone

  cone

outside of an event horizon the 3d projection of a `light cone` (all possible spacetime causality/light/info could observe) would be an omni-directional sphere - your own observable universe, essentially - composed of ever-reddening beam of causality, being drag thru the 4th dimension, time...which results in a cone

but inside of an event horizon, that cone is actually an ever-narrowing beam in an ever-increasing gravitational field, slowing on the 4-d axis too. all ending in one 'point'.

my point being that the waist is infinitesimally, but not actually infinitely, small.

  The cylinder I referred to is the outgoing side of the light cones at the horizon. The horizon itself is a lightlike surface. So the distinction you appear to be trying to draw here is simply invalid for a black hole horizon.

hawking radiation evaporates larger black holes more than smaller black holes. even if not the most testable (understatement), 4/3 * pi * r^3 where r gets smaller infinitesimally is a cone when plotted over the 4th dimension.

outside of the event horizon the "light cone" would "be" a "barely-parallel" "cylinder" yes.

the universe with all of its forever-unreachable parties outside each others sphere of causality would be like a 4-d porcupine ball.

   but it doesn't look like any actual physical model that I'm aware of.

these aren't exactly intuitive geometries XD

pdonis 10 months ago

Sorry, but your statements still don't describe an actual physical model.

> the 3d projection of a `light cone`

Is not well-defined.

> all possible spacetime causality/light/info could observe...your own observable universe

This is a past light cone. The light cone whose outgoing side is the event horizon of a black hole is a future light cone.

> inside of an event horizon, that cone is actually an ever-narrowing beam in an ever-increasing gravitational field, slowing on the 4-d axis too. all ending in one 'point'.

Nope, wrong.

> hawking radiation evaporates larger black holes more than smaller black holes

Wrong. The intensity of Hawking radiation goes like the inverse cube of the mass. Smaller holes radiate more than larger holes.

> these aren't exactly intuitive geometries

Yes, indeed. Which means you shouldn't be trying to understand them intuitively the way you are doing. You should be looking at the actual math.

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Jerrrrrrry 10 months ago
> the 3d projection of a `light cone` Is not well-defined.
A future light cone is a spherical* (Lorentz transformations count? idk kinda breaks the analogy) volume of space that's radius is light speed, c. Depending on the cosmological 'constant' either being 0±ε and/or photon decay/beta omission, all light cones may one day be one singular omega one, an island of universes of estranged galaxies of un-affecting causality, or a moot memory of eternal timeless iron.
a this 4d-cone's shadow (projection unto a lower plane) is a sphere, unless one deviates the cone or observation point from it's axis/dimension of projection, then it 'sharply' becomes a pointy-hemisphere, then a cone, as the projection approaches the perpendicular axis. This deviation is the effect of Lorentz transformation affect on spacetime. The higher the deviation, the closer to C, the more stretched the projection - space - becomes for an observer.
> inside of an event horizon, that cone is actually an ever-narrowing beam in an ever-increasing gravitational field, slowing on the 4-d axis too. all ending in one 'point'. Nope, wrong.
Care to explain how?
Once you cross the event horizon, your time will end in that same point, regardless of your movement in space.
This projection would be an ever-narrowing cone.
I appreciate the discourse, and I know projections/analogously breaking are the bane of the physicists, but I am wondering where my mental model is imprecise - at the edge of the impossible singularity, or the edge of the 'hairy' black hole?
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- pdonis 10 months ago
  
  > A future light cone is a spherical (Lorentz transformations count? idk kinda breaks the analogy) volume of space*
  No, it isn't. It's a 4-dimensional region of spacetime bounded by a null cone.
  > Care to explain how?
  What you think you know about all this is so far off base that I'm not sure where to start. Pretty much everything you've said has been wrong.
  > Once you cross the event horizon, your time will end in that same point, regardless of your movement in space.
  Wrong. The singularity is not a point. It's a spacelike line. Different people that fall through the event horizon separately will not meet each other at the singularity. In fact they will not even be able to see each other reach the singularity.
  > This projection would be an ever-narrowing cone.
  Wrong.
  > I am wondering where my mental model is imprecise
  It's not just "imprecise", it's wrong, pretty much everywhere. I would strongly suggest taking the time to look at some spacetime diagrams--the best ones would be a diagram in Kruskal coordinates or a Penrose diagram.
  
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