# Do Events Take Place Inside Black Holes?

As you approach a black hole, the universe you observe slows down. When you see someone from outside approaching a black hole, you see how they freeze in time as they get closer and closer to the event horizon. Their frame of reference slows down as seen from the outside. In fact, all of time passes for the observer far away from the black hole, before the other observer reaches the black hole ... or at least that's what I take away from it. (But tell me, please: Does this period of observation of everything (if this is the case at all) last for a long period of time (I'm thinking about exceeding the life span of a human) or (what I think is more likely to be true, from my "concept" of it) a very short period of time (a fraction of a second from some point in the future to all eternity)?)

Yet we know that black holes don't last for all eternity. They radiate away. Very slowly when they are big, but they do disintegrate and finally vanish in a finite amount of time.

If, before a black hole can be reached by things falling in, all of time passes (when observing the rest of the universe) and after some finite time there is no black hole any more, does this mean that no event can take place inside a black hole?

As you probably have figured out, I'm assuming that from the fact that time for the rest of the universe speeds up as you approach a black hole, it follows that an observer on the inside of the black hole experiences no time before either all of time has passed for the rest of the universe or until there is no more black hole. While I can imagine this to be true I never heard of this and can come up with a different hypothesis. However, this one seems more likely to me. Also, the other one would answer "no" to my question, so there's that.

• If you're asking about what happens to the information contained inside a black hole as it radiates away into nothing, then the answer is that no one knows. The leading proposals to resolve the information paradox are summarized succinctly on this wikipedia page en.wikipedia.org/wiki/Black_hole_information_paradox Commented Oct 8, 2015 at 1:24
• Commented Oct 8, 2015 at 11:04
• "You want to use a coordinate system that is regular at the horizon, like Kruskal-Szekeres". No, you don't. They will have you thinking the elephant goes to the end of time and back and is in two places at once. Commented Oct 8, 2015 at 13:27
• @emiliopisanty since the CMB cools as the universe expands, shouldn't black holes of any size cross the threshold from "big" to "small" and begin evaporating away? Or would we have to take limits of the black hole's rate of consumption vs. the CMB's rate of cooling to determine that? Commented Oct 8, 2015 at 15:56
• @UTF-8 "all of time passes for the observer far away from the black hole, before the other observer reaches the black hole..." you have two observers and thus two frames of reference. The observer at infinity sees the in-falling body slow down asymptotically as it approaches the horizon. The in-falling observer sees the universe at large speeding up infinitely before hitting the singularity in a rather short time. They don't both see "time slowing down" near the horizon: each observer, looking at his own watch, notes that it still keeps perfect time. Commented Oct 8, 2015 at 16:04

Of course time to collision is short, plus tide effects might tear matter appart. But "beside", in the local frame of the observer, nothing change: events still happen.

Anyway, take care about what you exactly call "black hole" ( Schwarzschild limit vs the central singularity in RG model alone vs the real-world "central thing"). If it is the Schwarzschild limit, then for giga black holes like the one at galaxy center nothing special happens for you at this limit (e.g., no significant tide effects), and you are still very far to the collision. So normal events still do occur for you.

• "even though it may be too small to measure": of course. -> edited to "no significant". Commented Oct 8, 2015 at 13:52

Events inside a black hole occur for observers at those events.

But those events cannot be assigned a physically meaningful time coordinate  – or “a when”, as put by Dr. Gabriel ‘Gabe’ Perez-Giz, (NYU/Princeton), in the video linked below – by an observer outside the black hole, so they do not occur for them.

In fact, he says, a black hole “is the set of all events that do not occur” for an observer outside that black hole. Which makes sense to me. After all, we consider the outer boundary of a black hole an event horizon.

Consider, for example, the Schwarzschild metric in Schwarzschild coordinates, which also describes a Schwarzschild black hole: a black hole whose electric charge is $$Q = 0$$ (“uncharged”, “electrically neutral”) and whose total angular momentum is $$J = 0$$ (“non-rotating”). It can be written (using sign convention $$(+, -, -, -)$$)

$${\mathrm ds}^2 = \left(1 - \frac{\mathrm r_\text S}{r}\right) {\mathrm c}^2{\mathrm dt}^2 - {\left(1 - \frac{\mathrm r_\text S}{r}\right)}^{-1} \, {\mathrm dr}^2 - r^2 \left[{\mathrm d\theta}^2 + \sin^2(\theta) \, {\mathrm d\varphi}^2\right],$$

where

$$\mathrm r_\text S = \frac{2 \, \mathrm G \, \mathrm M}{{\mathrm c}^2}$$

is the Schwarzschild radius; for a Schwarzschild black hole, the radius of its outer event horizon or simply its radius. ($$\mathrm M$$ is the black hole’s “mass”; see the video below for details.)

If you consider events with $$r < \mathrm r_\text S$$, i.e. inside that black hole, you can see that

$$\frac{\mathrm r_\text S}{r} > 1 \implies 1 - \frac{\mathrm r_\text S}{r} < 0,$$

which means

$$\left(1 - \frac{\mathrm r_\text S}{r}\right) {\mathrm c}^2{\mathrm dt}^2 < 0$$ and $$-{\left(1 - \frac{\mathrm r_\text S}{r}\right)}^{-1} \, {\mathrm dr}^2 > 0.$$

But the signs in the metric have a physical meaning: Previously we had chosen the sign convention such that the spacetime interval $${\mathrm ds}^2$$ between timelike-separated events (that can be connected by motion with a relative speed less than $$\mathrm c$$) would be positive, and between spacelike-separated events (that cannot) it would be negative.

Now, inside the black hole, events that would be timelike-separated are (according to our convention) spacelike-separated, and vice-versa. So we cannot reasonably say that proper time elapses on a path connecting the former events. Therefore, we cannot assign a physically meaningful time coordinate to them, which is to say that for an observer outside that black hole – us, who are aware that there is a black hole –, they do not occur.

[There are other coordinates in which the Schwarzschild metric can be written, for example Gullstrand–Painlevé and Kruskal–Szekeres coordinates. But ISTM that the temporal coordinate there does not have a physical meaning; it is just a mathematical trick to avoid the coordinate singularity that appears in Schwarzschild coordinates at $$r = \mathrm r_\text S$$.]

Furthermore, I think that, if we use the fact that light from events inside the black hole cannot reach an observer outside as a guide, even events inside a Schwarzschild black hole do not occur for observers inside such a black hole who are at reception events whose angular coordinates ($$\theta$$ and $$\varphi$$) are not exactly equal to that of the emission event, as light from those events has to fall radially inward. This might be different for a Kerr or Kerr–Newman ("rotating") black hole.

(CMIIW)

And, I have to point out that, given its title, you could have found the first video at the time of posting already by a Web search, by simply entering your question there.

Do Events Take Place Inside Black Holes?

Opinions vary. If you have a look at the Mathpages formation and growth of black holes you can read about two interpretations:

"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches "full stop" (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence."

Most people only know of the other interpretation, where the infalling body goes through the event horizon. From what I know of general relativity, I'd say that's wrong, and that the correct interpretation is the one where everything stops at the event horizon.

As you approach a black hole, the universe you observe slows down. When you see someone from outside approaching a black hole, you see how they freeze in time as they get closer and closer to the event horizon. Their frame of reference slows down as seen from the outside. In fact, all of time passes for the observer far away from the black hole, before the other observer reaches the black hole ... or at least that's what I take away from it.

Me too. Gravitational time dilation goes infinite. Many people will tell you the Schwarzschild event-horizon singularity is a mere artefact, and that you can adopt another coordinate system to do away with it. I disagree with that, and say that Kruskal-Szekeres coordinates commit the schoolboy error of putting a stopped observer in front of a stopped clock and claiming that he sees it ticking normally.

Yet we know that black holes don't last for all eternity. They radiate away.

No, we don't know that. Hawking radiation remains hypothetical. Moreover the "given" explanation has particles popping into existence, negative energy particles, and no gravitational time dilation. I think it's unsatisfactory.

If, before a black hole can be reached by things falling in, all of time passes (when observing the rest of the universe) and after some finite time there is no black hole any more, does this mean that no event can take place inside a black hole?

I think no event can occur because its a place where gravitational time dilation is infinite and the "coordinate" speed of light is zero. Not because the black hole somehow disappears.

It follows that an observer on the inside of the black hole experiences no time before either all of time has passed for the rest of the universe or until there is no more black hole.

Agreed.

While I can imagine this to be true I never heard of this

Google on Oppenheimer frozen star and you can read about it. I'm afraid what sometimes happens in physics is that the people who promote a particular interpretation want you to think its the only interpretation, and that what they say cannot be challenged.