Black hole ramblings

In My Humble Opinion
21

According to that wiki link that is mass loss.

When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by Einstein’s equation E = mc 2). Consequently, an evaporating black hole will have a finite lifespan. By dimensional analysis, the life span of a black hole can be shown to scale as the cube of its initial mass,[18][19]:176–177 and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 1015 g would have evaporated completely by the present day.[20]

In 1976, Don Page refined this estimate by calculating the power produced, and the time to evaporation, for a nonrotating, non-charged Schwarzschild black hole of mass M.[18] The calculations are complicated by the fact that a black hole, being of finite size, is not a perfect black body; the absorption cross section goes down in a complicated, spin-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Page concluded that primordial black holes could only survive to the present day if their initial mass were roughly 4×1014 g or larger. Writing in 1976, Page using the understanding of neutrinos at the time erroneously worked on the assumption that neutrinos have no mass and that only two neutrino flavors exist, and therefore his results of black hole lifetimes do not match the modern results which take into account 3 flavors of neutrinos with nonzero masses. A 2008 calculation using the particle content of the Standard Model and the WMAP figure for the age of the universe yielded a mass bound of (5.00±0.04)×1014 g.[21]

If black holes evaporate under Hawking radiation, a solar mass black hole will evaporate over 1064 years which is vastly longer than the age of the universe.[22] A supermassive black hole with a mass of 1011 (100 billion) M☉ will evaporate in around 2×10100 years.[23] Some monster black holes in the universe are predicted to continue to grow up to perhaps 1014 M☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10106 years.[22]

22

At a quantum level, energy and mass are indistinguishable. We heard that from some Swiss patent clerk.

23

So black hole evaporation means it loses mass. Which sort of implies the mass is not chilling in a singularity.

24

It’s a bit of a nitpick, but it’s not quite accurate to say that it implies some form of nonlocality/FTL influence. Bell’s theorem produces the conclusion that only if you assume that there are beforehand values to all observable quantities, these values must influence one another instantaneously across arbitrary distances. But we don’t need to make that assumption.

Now, some people (including some people educated in such matters) believe that the Einstein-Podolsky-Rosen argument implies the existence of such values. If that were the case, then Bell inequality violations would certify nonlocal influences. But most people, myself among them, don’t think this is right (incidentally, that paper contains what I think is the simplest proof of Bell’s theorem, which shows that its mathematical content really is just the nonexistence of a joint probability distribution for all observable quantities).

While that’s sometimes a useful idealized picture, one shouldn’t rely on it too much, as it gives wrong results if taken too literally. For one, what’s emitted in Hawking radiation isn’t really localized, but spread out to a degree comparable to the black hole radius, so it’s not really meaningful to consider this as the result of some form of pair production at the event horizon; and indeed, tracing the radiation back to a putative horizon-based origin leads to enormous blueshift, and thus, high temperature at the horizon, in violation of the equivalence principle.

It’s more accurate to say that different observers have different notions of particles. An accelerating observer in flat space-time, for instance, will also observe radiation, while a stationary one won’t; this is the Unruh effect, and it’s conceptually highly similar to Hawking radiation. In fact, you can get Hawking radiation from the Unruh effect, by noting that an observer close to the horizon needs to accelerate to keep from falling in.

Not to anybody’s knowledge. In fact, renormalization is a problem when it comes to gravity: the most simple way to quantize gravity leads to a theory that’s non-renormalizable.

No matter (or radiation) is ever lost, as in, crosses the horizon. Mass is certainly lost.

That’s got nothing to do with the ‘quantum level’. Also, it’s not that energy and mass are indistinguishable—mass really is just that energy of the system that can’t be removed by changing reference frames, as, for instance, kinetic energy can, by just going to the system in which something is at rest.

25

How do you calculate Ek though? I mean, everything is in motion. If you and I are flying through space at really fast and I give you a little kick, now you are at really fast + 1 and I am at really fast - 1 (with adjustments for our changed vectors). Everything else around us is going pretty close to really fast, so our relative EK is quite low.

But what about that one thing over there that is going very much not as fast? My little kick has diverted me to a collision course with slower thing. When that happens, pieces of it and me will be going a lot of different speeds in different directions, conserving our relative net energy. A few of those pieces will probably hit you.

Meanwhile, you are nudged into a collision course with this other thing, but it is also going really fast on a similar vector to you, so your net energy will be very low, even though you are both going really fast, so you will just bump gently into each other. Unless, of course, it is really big and you crash into it because of its gravity.

Arrgh, this math is hard.

26

A true union is The Borg, and few people would like that (I guess).

27

Not sure what you mean, here. You can use whatever system is most convenient/relevant for you. For instance, if you collide two little ball bearings on a rail, you might take the system of the laboratory, in which both balls move towards one another, or you might take the system in which one is at rest—but you’ll get, as a result, always the motion within that system after the collision.

28

The Borg queen was bald and her complexion was terrible so, no, I wouldn’t like that! LOL

29

It reaches a standstill from OUR perspective OUTSIDE of the Black Hole because of Time Dilation. In Einstein’s Theory of Relativity, the people inside of a spaceship traveling at 90% of the speed of life would experience a “normal” passage of time specific to their own environment. That implies that, inside of a Black Hole, we cannot apply the standard you are using to support your theory. Gravity is gravity, and I see no reason to assume that particle collapse would simply cease based on what we see outside of the Black Hole.

30

Nah, you’re thinking of quantum discord…

31

So, do black holes matter, or do black holes anti-matter? Or, is it both?

32

Whew! I thought sure somebody would come by to smack me around for making a “black holes anti-matter” joke!

33

I am curious about this.

Consider the perspective of the particle/person falling in. Time does not stop for it but it will see the rest of the universe accelerate in time…like it is in fast forward. Presumably, at the event horizon, time in the distant universe passes by so quickly the universe itself will end in an instant. If so then wouldn’t the BH also zoom out of existence?

To an outside observer all of this would take uncountable ages to happen but for you…poof.

What time then to get inside the black hole and find the singularity?

34

If you are freely falling, then you would not have this experience. Sure, the universe is “speeding up” around you, but you are not seeing this, as you are retreating from it at greater than light speed yourself. It appears to be slowing down and redshifting, from your perspective.

According to straight up relativity, you should notice nothing out of the ordinary when you cross the event horizon. Space itself is being dragged in, and you along with it. Once you have gone a little ways in, the bit of space that is further out will never be able to catch up with you, as you will be moving away from it at greater than lightspeed.

The universe would actually become redshifted and disappear to you, just as you have redshifted and disappeared to an outside observer, as you plummet to your own doom.

Plus side, you might get to find out what happens at the “singularity”. Down side, you won’t know for very long, and won’t be able to share it with anyone. I can’t find it now, but I think it was on this board that someone cited an article where someone calculated the proper time to hit the singularity, and it was somewhere on the order of 90 seconds for a super massive black hole.

35

There is certainly an interesting paradox between the apparently infinite “frozen forever” time dilation at the event horizon as observed from an outside frame of reference and the fact that in the proper time of an infalling object it passes through the EH and reaches the singularity in a matter of seconds or minutes, depending on the size of the black hole. You may be interested in this thread, if you haven’t already seen it, which makes some interesting points about this paradox.

I posted some thoughts about it in posts #18 and #22. There’s also a good response by @Asympotically_fat in post #25.

36

So I read some of that (@wolfpup too) and I still have questions:

From the reference frame of the person falling in they will always see their watch pass at 1 second per second. From the reference frame of a distant observer the person falling has their watch slow down and they never see them pass the event horizon…rather just fade away.

Does the person falling in share a reference frame with the entire black hole? If not then is it possible that nothing ever truly passes the event horizon and the black hole has a shell of matter it has gathered over time at what we call the event horizon?

Consider:

Regardless of what it looks like to you as you fall towards the black hole it remains that time slows down for you compared to the outside universe (even if it all seems normal to you). So much so that the distant universe will speed to an end before you ever cross the event horizon.

Also, if your frame of reference is not the same as the black hole (which I do not think it would be) then as time slows for you the black hole itself will speed forward in time and shrink via Hawking Radiation.

I realize that is a really slow process but since we are getting arbitrarily close to time stopping for the person falling in they have the time. To them the event horizon would forever be just out of reach as it shrinks. As the BH shrinks the event horizon moves away a bit and the person falling in clock speeds up a bit and they move closer then slow down till it moves away…there would be a balance here.

The person falling in reaches the singularity at the moment it poofs out of existence (along with them presumably).

I hope that makes some sense.

37

Assuming that their watch is arbitrarily close to their eyes, yes.

No. You would only share the reference frame with stuff arbitrarily close to you. At some point, you won’t even share it with your watch, as your body is ripped apart by tidal forces.

Probably not. But here we get back to the firewall hypothesis.

Space itself is being pulled into the black hole at the speed of light at the event horizon. There is nothing in relativity that would indicate that anything stops at that point.

Your internal clock is slowing down. Your velocity towards the “singularity” is not. You don’t slow down in your fall towards the event horizon as you get close, it’s just that if an outside observer was watching your clock, they would see it slow down. They would not see your velocity decrease, just your clock. To you, it would seem as though you were speeding up even more, as your perception of time slows down.

Now, to some extent, your ignorant observer may think that they have not crossed the event horizon, as there will always be in front of them a growing sphere that no light can reach them from. At some point, it stops being only “below” you, and starts reaching up and around you, eventually enveloping you in a sphere that no light can catch up to and enter.

Now, the “singularity” itself would always be out of reach. The black hole in the center of our galaxy measures as around 14 million km across, but that’s in flat space, something that you don’t get to take for granted in a black hole. The actual distance to the singularity would be much, much further.

The idea that you would “reach” the “singularity” at the same time as the black hole finishes evaporating is not unrealistic, but is not necessarily the case, either.

The way to look at it from the holographic perspective is that, when you reach the event horizon, rather than seeing you stay at one point, an observer (with godlike observation powers) would actually see you smeared across the horizon. As you go deeper into the black hole, the amount of smearing increases. At the point that you reach the singularity, your information has become smeared evenly across the event horizon.

38

Everything in physics is an approximation. Statements like that an infalling object, from an outside perspective, are frozen at just outside the event horizon, are based on an approximation that the black hole itself is static. That approximation certainly breaks down if you wait long enough for the black hole to evaporate, and probably long before then. So what does actually happen in such a case? You’d need a more detailed model to answer.

Both, or neither, or more precisely irrelevant. A black hole formed from matter is completely indistinguishable from one formed from antimatter, or from a mix of both, or from light (yes, you can form a black hole from light). And no matter how it forms, if you let it evaporate, it’ll eventually release approximately equal amounts of matter and antimatter (plus light and gravitons and other things that can’t really be considered either).

39

And you have to wait quite a long time before the black hole even starts to evaporate, as anything but the tiniest of primoradial black holes (if they exist) are considerably cooler than the cosmic microwave background.

40

I think it is important to realise the concept of extended reference frames, whislt useful, do not have physical meaning- they are cooridnate systems. Therefore you need to be careful about drawing physical conclusions from them.

You can construct a frames based on a faraway observer and you can construct frames based on an infalling observer. Neither should be given priority.

What observers ‘see’ is physical, however observations of a faraway object don’t just depend on the properties of the observed object, so again you must be careful about what conclusions you draw.

We can say definitively for a Schwarzschild balck hole that, if an event on the event horizon and an event outside the event horizon have a past-future relationship, then the event on the event horizon is the future event. However for any event on the event horizon there will be events outside where there is no past-future relationship. That is why you cannot objectively say that all events outside are in the past to an observer crossing the event horizon.

If we look at a black hole evaporating due to Hawking radiation the spacetime structure is different so in fact events on the event horizon can be in the past of events outside. Events within the evnt horizon though still cannot be in the past of events outside.

If we model the evaporation by hand and so ignore any possible bizarre quantum effects like firewalls, then the experience of an infalling observer is pretty much as before. They will cross the event horizon and a short time later hit the singularity. Whislt in the event horizon it will not see the entire history of the outside region.

For a farway observing and infalling object in to a an evpaorting black hole it will intially proceed as before. The infalling observer will appear to slow down as it reaches the event horizon, never quite reaching it. However when the shrinking of the evnt horizon is signifcant the infalling observer will still appear to be approaching the evnt horizon and will actually be observed to cross the event horizon at the very moment that the black hole is observed to evaporate completely. The outside observer though still won’t see what happened once the object crossed the hroizon.