The firewall paradox of black holes talks about an observer falling through the event horizon and still performing observations after passing the horizon.
https://www.sciencemag.org/news/2007/06/no-more-black-holes
But in the Schwarzschild solution it is easy to calculate that in the global Schwarzschild coordinate time it takes an infinite time for the astronaut to reach the event horizon. Lawrence Krauss in the above link talks about this.
Do we have any reason to assume that the fall of the astronaut continues longer than the infinity of the global Schwarzschild time?
We do not see any reason for such an assumption. The astronaut will "freeze" just above horizon. His proper time will not continue past the finite proper time it takes for him to reach the horizon.
https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates
The popular belief that the astronaut would be able to pass the horizon is based on the Gullstrand-Painleve coordinates where the flow of time is the proper time of the astronaut. Does it make sense to extend the proper time of the infalling observer past the infinite time of the global Schwarzschild coordinates? Suppose that the universe will end by some mechanism before an infinite time has passed. Then the astronaut would be wiped out before he reaches the event horizon.
Gullstrand and Painleve introduced their coordinates to argue that the Einstein theory is nonsensical because the "singularity" of the Schwarzschild coordinates at the event horizon can be removed with their coordinates. But their coordinate system does not make sense if the age of any part of the universe cannot be "greater than" infinity.
Note that since no true event horizon ever forms, there is no genuine singularity in the Schwarzschild coordinates at the event horizon.
Later, the Gullstrand-Painleve coordinates were used in popular science books to introduce the model where an observer can fall past the event horizon.
Since nothing will ever go past the event horizon, there cannot be any firewall paradox. There is no duplication of quantum information at the horizon.
The information loss paradox of black holes does not exist either. The paradox was how the information devoured by a black hole can be returned in seemingly random Hawking radiation. In this blog we have argued that Hawking radiation probably does not exist because it would break basic principles of quantum physics. Now we have another argument which removes the information loss paradox: the black hole never "devours" anything. The information is preserved in the infalling matter which never reaches the horizon.
Several authors (e.g., Lawrence Krauss in the sciencemag.org link above) have previously noted that the hypothetical Hawking radiation would make the black hole to evaporate before anything can reach the event horizon.
If we let a dust sphere collapse on a star, and there is enough mass that the star and the sphere would form a black hole, then the proper time inside the forming horizon will essentially stay still once the dust sphere is close to the horizon. No singularity of infinite density will ever form. The star inside the horizon is frozen at its place.
A singularity in Einstein's equations would be ugly because the equations are not defined at such a point. Fortunately, no singularity ever forms.
Did Einstein write anything about this? He tried to show that black holes cannot form in astrophysics, but did he comment on the Gullstrand-Painleve coordinates?
https://www.sciencemag.org/news/2007/06/no-more-black-holes
But in the Schwarzschild solution it is easy to calculate that in the global Schwarzschild coordinate time it takes an infinite time for the astronaut to reach the event horizon. Lawrence Krauss in the above link talks about this.
Do we have any reason to assume that the fall of the astronaut continues longer than the infinity of the global Schwarzschild time?
We do not see any reason for such an assumption. The astronaut will "freeze" just above horizon. His proper time will not continue past the finite proper time it takes for him to reach the horizon.
https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates
The popular belief that the astronaut would be able to pass the horizon is based on the Gullstrand-Painleve coordinates where the flow of time is the proper time of the astronaut. Does it make sense to extend the proper time of the infalling observer past the infinite time of the global Schwarzschild coordinates? Suppose that the universe will end by some mechanism before an infinite time has passed. Then the astronaut would be wiped out before he reaches the event horizon.
Gullstrand and Painleve introduced their coordinates to argue that the Einstein theory is nonsensical because the "singularity" of the Schwarzschild coordinates at the event horizon can be removed with their coordinates. But their coordinate system does not make sense if the age of any part of the universe cannot be "greater than" infinity.
Note that since no true event horizon ever forms, there is no genuine singularity in the Schwarzschild coordinates at the event horizon.
Later, the Gullstrand-Painleve coordinates were used in popular science books to introduce the model where an observer can fall past the event horizon.
There is no firewall paradox or information loss paradox
Since nothing will ever go past the event horizon, there cannot be any firewall paradox. There is no duplication of quantum information at the horizon.
The information loss paradox of black holes does not exist either. The paradox was how the information devoured by a black hole can be returned in seemingly random Hawking radiation. In this blog we have argued that Hawking radiation probably does not exist because it would break basic principles of quantum physics. Now we have another argument which removes the information loss paradox: the black hole never "devours" anything. The information is preserved in the infalling matter which never reaches the horizon.
Several authors (e.g., Lawrence Krauss in the sciencemag.org link above) have previously noted that the hypothetical Hawking radiation would make the black hole to evaporate before anything can reach the event horizon.
There is no singularity inside the event horizon
If we let a dust sphere collapse on a star, and there is enough mass that the star and the sphere would form a black hole, then the proper time inside the forming horizon will essentially stay still once the dust sphere is close to the horizon. No singularity of infinite density will ever form. The star inside the horizon is frozen at its place.
A singularity in Einstein's equations would be ugly because the equations are not defined at such a point. Fortunately, no singularity ever forms.
Did Einstein write anything about this? He tried to show that black holes cannot form in astrophysics, but did he comment on the Gullstrand-Painleve coordinates?
An ever-slowing computer
Imagine a computer whose clock speed is decreasing in a way that it will only complete a finite number N of cycles during the infinite age of the universe. We may define the proper time of the computer to be the number of the completed cycles.
Does it make sense to build a physical model of the computer past the infinite age of the universe? In the model, the computer would keep crunching numbers at cycles N + 1, N + 2, and so on. The model does look nice. But the model does not make sense physically, if we assume that there is no universe "after" an infinite time has passed.
Why would we then use the Gullstrand-Painleve coordinates to extend time past the infinite time of the global Schwarzschild coordinates?
What happens to infalling matter according to optical gravity?
In this blog we have developed a new interpretation of general relativity where we assume that spacetime itself is a flat Minkowski space, but the strength of forces and the inertial mass of energy change according to the location in (Schwarzschild) coordinates.
Specifically, the speed of light slows down close to the event horizon and would be zero at the horizon if the horizon would form.
A zero speed of light in optics means an infinite optical density. All light would in this analogy model be reflected from the horizon.
But what happens to particles with a non-zero rest mass? They do not have enough energy to escape. Maybe those particles will keep bouncing off from the horizon, at the same time losing their kinetic energy to radiation.
If the local conditions close to the horizon have a great density of hot particles, then some unknown mechanism might be able to convert all particles to massless ones, and eventually all mass-energy would be reflected from the event horizon. The forming black hole would evaporate through a mechanism which is different from the hypothetical Hawking radiation. Information would be preserved. There is no information loss paradox in this scheme.
Kerr black holes
A rotating mass solution of the Einstein equations is much more complicated than the Schwarzschild solution.
Wikipedia mentions that the stability of the "internal" Kerr solution is not known. But if proper time is almost frozen inside some horizon of the Kerr solution, maybe there is no problem in this?
Implications for quantum gravity
The Gullstrand-Painleve coordinates show that, classically, there is no "drama" at the event horizon. The astronaut would not meet any high-energy phenomena as he approaches the event horizon. If we believe this classical scheme, then we can model everything with our current combination general relativity and quantum mechanics. There is no need for quantum gravity which would conceptually unify the two theories.
But the wave nature of matter suggests that the curved geometry close to the event horizon will make particles reflect at essentially the speed of light back from the horizon area. The astronaut will encounter particles of extremely high energies.
Also, the reflection process of quantum mechanical waves from curved spacetime requires us to develop a combined theory of gravitation and quantum mechanics, at least a semi-classical one.
Our blog post in the last fall showed that the reflection process of light waves from material of variable optical density (e.g., glass) is poorly understood, even though we can make empirical tests in the laboratory. In the case of curved spacetime, we only have empirical observations from the bending of light in the gravitational field of galaxies and stars. Reflection in these astronomical setups is negligible. In the case of black holes, reflection might produce effects that could be visible in the accretion disk. We need to develop models to estimate matter and light behavior close to the event horizon.
https://arxiv.org/abs/1612.00266
Niayesh Afshordi and others claim to have observed gravitational wave reflection from the the event horizon. Further events from the LIGO will reveal if the correlation they observed was real.
We believe that curved spacetime at the event horizon will cause reflection of gravitational waves as well as any other waves, but we do not have a mathematical model yet to calculate what the reflections should look like.
https://arxiv.org/abs/1612.00266
Niayesh Afshordi and others claim to have observed gravitational wave reflection from the the event horizon. Further events from the LIGO will reveal if the correlation they observed was real.
We believe that curved spacetime at the event horizon will cause reflection of gravitational waves as well as any other waves, but we do not have a mathematical model yet to calculate what the reflections should look like.
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