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Let’s say you fell into a rotating black hole, the inner horizon of the black hole is an infinite blue shift surface, so you should be able to observe events from the arbitrarily far future before reaching it.

I’ve heard that hawking radiation results in positive energy particle escaping the bock hole, while causing negative energy particles to fall In, what would this look like from the inside.

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    $\begingroup$ The Kerr geometry is an ideal solution that is believed to be unstable wrt perturbations caused by infalling matter, so it probably doesn't exist in the real world. The inner horizon and the region within it probably don't exist. $\endgroup$ Jul 30, 2023 at 18:55
  • $\begingroup$ I’m taking about what is observed just before reaching it $\endgroup$ Jul 30, 2023 at 18:59

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… so you should be able to observe events from the arbitrarily far future before reaching it.

This is wrong for “almost inertial” observers inside the outer horizon (i.e. observers whose trajectories do not deviate much from inertial trajectories of bodies falling into the black hole). Recall, that the black hole inner horizon has two components, “outgoing” and “ingoing”. The Cauchy horizon dependent on the entirety of future history is the ingoing component, but a particle falling from the outside would cross the outgoing component. So, unless you are in a spaceship capable of achieving relativistic velocities in a short time of order $r_g/c$, the ingoing component is inaccessible to you. On the other hand, if you do have a spaceship capable of ultrarelativistic velocities, there is no need for a black hole if you wish to see the distant future: ordinary flat space twins paradox suffices. The misconception ultimately originates from the use of Penrose diagrams for reasoning about spacetime structure. While such diagrams are great for considering causality, they depend on the conformal structure of spacetime and do not retain information about lengths, durations, momentum changes etc.

Having said that, the question of what happens to the Hawking radiation at the inner horizon has indeed been studied by several groups in the last few years: one, two, three, four, five. The papers convey a picture of quantum divergencies that observers would encounter near the (would be) inner horizon, independent from classical instabilities developing there.

The most accessible source would be the essay

  • McMaken, T. (2023). Pancakification and negative Hawking temperature, arXiv:2305.09019.

Here are some quotes:

… one of the key insights we wish to convey here is that the miniscule levels of Hawking radiation that manage to leak out to infinity are nothing compared to the roiling atmosphere of quantum radiation near the inner horizon.

An observer falling into a black hole will be met with an increasingly dense atmosphere of Hawking radiation as they plunge through the interior until they reach a wall of infinite energy at the inner horizon.

But once the observer approaches the inner horizon, the spectrum no longer appears Planckian. Instead, the exponential drop-off at high frequencies inverts, leading to an ultraviolet divergence. As shown by the dashed curves, these spectra approximately match the magnitudes one would obtain for a Planckian distribution with negative temperatures $\kappa_\text{eff} ^{−}/(2\pi)$ and $\kappa_\text{eff} ^{+}/(2\pi)$ at the left and right inner horizons, respectively …

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  • $\begingroup$ I half suspected it would be like this. $\endgroup$ Jul 31, 2023 at 19:27
  • $\begingroup$ Isn’t it true and quite self evident that a black hole created by a physical collapse would evaporate before anything can cross the horizon? This diagram i.stack.imgur.com/677y2.jpg shows coordinate timeslices. The red line is when the black hole evaporates and no longer exists anywhere above this line. Any event of crossing the horizon is above this line and thus cannot happen since by then there is no black hole. Where is a logical flaw in this argument? $\endgroup$
    – safesphere
    Aug 1, 2023 at 8:28
  • $\begingroup$ Thanks for an interesting (now deleted) discussion! To summarize, my point has been that the black hole evaporation event is in the past light cone of every falling observer while he is still outside. This means the black hole ceases to exist before anything can cross the horizon in any coordinate system, so nothing is ever inside. Your objection is that the Hawking radiation breaks the external-only causality, but you have not clarified why this implies the existence of the “inside”, as opposed to, say, a firewall just outside the horizon. $\endgroup$
    – safesphere
    Aug 3, 2023 at 17:12

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