- #1
Tomas Vencl
- 66
- 13
- TL;DR Summary
- Thinking about statement “In a evaporating spacetime it does not take an infinite amount of coordinate time to cross the horizon in Schwarzschild-like coordinates”
Here is first principles consideration:
Since it is a black hole there is an event horizon where timelike worldlines can enter but not exit, this is what defines a black hole instead of a white hole. When evaporation is finished there is no more event horizon, this is what defines the evaporation. Without loss of generality, assign the time of the evaporation event to be . Meaning, after there is no event horizon. All coordinate charts, by definition, are smooth and one-to-one, including the distant observer's Schwarzschild-like chart. So the crossing of the event horizon cannot be assigned a time coordinate . Therefore, indeed, it does not take an infinite amount of coordinate time to cross the horizon.
I was thinking about what it even means in the light of first principles to say that in Schwarzschild-like coordinates, an infalling worldline crosses the horizon of an evaporating black hole in finite coordinate time. Since we don’t know the metric, I don’t expect us to find an exact answer, but rather an attempt to see if we can infer anything more from these first principles.
Does this claim mean that we can map the geodesic of an infalling object even below the horizon in Schwarzschild coordinates? Isn’t one of the key properties of the horizon that it is uncrossable in Schwarzschild coordinates? If it loses this property, what other property defines it as a horizon?
One can think about some strange quantum effects on the infalling observer or on the metric, but that would imply that these effects must be dramatic already near the horizon, which is contrary to the generally accepted assertion that from the perspective of the falling observer, nothing dramatic happens during the passage through the horizon.
I am following up on a neighboring thread and for that reason, I don’t want to place the question in the ‘beyond the standard model’ section, but feel free to be more speculative and heuristic. I don’t expect a solution, rather your perspective on the matter. Thank you.
Since it is a black hole there is an event horizon where timelike worldlines can enter but not exit, this is what defines a black hole instead of a white hole. When evaporation is finished there is no more event horizon, this is what defines the evaporation. Without loss of generality, assign the time of the evaporation event to be . Meaning, after there is no event horizon. All coordinate charts, by definition, are smooth and one-to-one, including the distant observer's Schwarzschild-like chart. So the crossing of the event horizon cannot be assigned a time coordinate . Therefore, indeed, it does not take an infinite amount of coordinate time to cross the horizon.
I was thinking about what it even means in the light of first principles to say that in Schwarzschild-like coordinates, an infalling worldline crosses the horizon of an evaporating black hole in finite coordinate time. Since we don’t know the metric, I don’t expect us to find an exact answer, but rather an attempt to see if we can infer anything more from these first principles.
Does this claim mean that we can map the geodesic of an infalling object even below the horizon in Schwarzschild coordinates? Isn’t one of the key properties of the horizon that it is uncrossable in Schwarzschild coordinates? If it loses this property, what other property defines it as a horizon?
One can think about some strange quantum effects on the infalling observer or on the metric, but that would imply that these effects must be dramatic already near the horizon, which is contrary to the generally accepted assertion that from the perspective of the falling observer, nothing dramatic happens during the passage through the horizon.
I am following up on a neighboring thread and for that reason, I don’t want to place the question in the ‘beyond the standard model’ section, but feel free to be more speculative and heuristic. I don’t expect a solution, rather your perspective on the matter. Thank you.