- #1
OJ Bernander
- 7
- 7
- TL;DR Summary
- Dustball collapse is transformed to standard coordinates. The shrinkage speed of the Schwarzschild radius is much larger than the internal coordinate speed of light.
This old nut is often dismissed as flawed thinking by a naive student. It’s been discussed here too, I know.
However, when you do the math in standard (Schwarzschild-like) coordinates:
Dustball collapse and evaporation in standard coordinates (Arxiv)
A. the (coordinate) speed of light inside a collapsing star is much smaller than outside,
B. the speed at which the Schwarzschild radius shrinks (by evaporation) is intermediate between the two.
Therefore if we perturb the classical solution with an evaporation process at the (shrinking) Schwarzschild radius:
1. the perturbation only spreads to the exterior, not the interior, limited by c,
2. the singularity is not in the part of the (interior) solution that survives,
3. infalling particles don’t cross the Schwarzschild radius,
4. outgoing photons are temporarily frozen, but eventually emerge (no horizon forms).
The analytic work shows A and B. Then 1-4 follow.
I’ve seen others speculate on 1-4, but not back it up with A and B.
Such speculation is often dismissed, using intuition from non-evaporating black holes.
A and B should correct the flawed intuition where it doesn’t apply to evaporating collapse.
Thoughts?
-Öjvind
(I have read the discussion here on PF)
However, when you do the math in standard (Schwarzschild-like) coordinates:
Dustball collapse and evaporation in standard coordinates (Arxiv)
A. the (coordinate) speed of light inside a collapsing star is much smaller than outside,
B. the speed at which the Schwarzschild radius shrinks (by evaporation) is intermediate between the two.
Therefore if we perturb the classical solution with an evaporation process at the (shrinking) Schwarzschild radius:
1. the perturbation only spreads to the exterior, not the interior, limited by c,
2. the singularity is not in the part of the (interior) solution that survives,
3. infalling particles don’t cross the Schwarzschild radius,
4. outgoing photons are temporarily frozen, but eventually emerge (no horizon forms).
The analytic work shows A and B. Then 1-4 follow.
I’ve seen others speculate on 1-4, but not back it up with A and B.
Such speculation is often dismissed, using intuition from non-evaporating black holes.
A and B should correct the flawed intuition where it doesn’t apply to evaporating collapse.
Thoughts?
-Öjvind
(I have read the discussion here on PF)