What's really down in a BH? (a Planck star)

[marcus]

Planck star is a proposed new idea which, if it gains support, will change how we think about "black holes".

One can think of a Planck star as a slow-motion bounce that because of extreme time-dilation can take hundreds of billions of years to mature. When it finally does, the star breaks through its trapping horizon outer shell and dissipates in an explosion.

The concept arises in Loop gravity theory. As a general rule at extremely high densities a quantum correction appearing in Loop gravity causes gravity to repel rather than attract, so that "collapse to singularity" is replaced by BOUNCE. You can think of a Planck star as the final stage in the life of a massive star, even denser than a neutron star. In the Loop picture, it takes the place of the "singularity" in the classical BH picture.

A Planck star is so dense that it creates a trapping HORIZON around itself, analogous to the "event horizon" of a classical Schwarzschild black hole. It is an object so dense that
1. the local proper time is greatly SLOWED, an outside observer somehow able to witness it would see collapse and bounce happen with such glacial slowness that it would seem FROZEN to the outsider

2. but no outsider can witness this slow-motion bounce because the Planck star has created a trapped region around itself, from which light cannot escape. However the trapping horizon can emit Hawking radiation, and the Planck star will also eventually explode.

Radiation and eventual explosion.

Like the "event horizon" of a conventional black hole, the Planck star's outer trapping horizon emits HAWKING RADIATION. One can think of that as pairs of virtual particles one of which flies outward while the other falls inward giving up gravitational energy in the process. The total mass is reduced by Hawking radiation and the outer trapping horizon gradually shrinks.

Meanwhile the Planck star itself, which is at the center of this spherical trapping horizon, is gradually expanding and will eventually burst through it in an end-of-life explosion.

To get more detail, simply google "planck star". You will get an arxiv preprint of the "Planck stars" article posted by Rovelli and Vidotto. BTW Francesca Vidotto is a longtime PF member who used to post a lot here when she was still a student.

 

[marcus]

The relevant for astrophysics is twofold:

1. Using the Planck star model one can calculate the expected lifetime of a Planck star from its initial mass. So one can estimate the masses of primordial ones which should have already exploded. If the phenomenon is valid, this will have left a calculable IMPRINT on the spectrum of cosmic rays.
2. The Planck star concept, if confirmed, helps complete our idea of the life histories of stars. How stars end depends on their mass---the least massive simply become cooling white dwarves, moderately massive can leave a neutron star remainder, cores of those still more massive may collapse to form Planck stars.
3. It also offers the possibility of a more realistic picture of a black hole. The idea of "singularity" (where GR breaks down, time stops, and curvature blows up) is unphysical and unsatisfactory for various reasons. So here we have a chance of replacing the singularity with something physical in our black hole picture.

I should get the link to the paper. (just by googling "planck stars")
http://arxiv.org/abs/1401.6562
Planck stars
Carlo Rovelli, Francesca Vidotto
(Submitted on 25 Jan 2014 (v1), last revised 28 Jan 2014 (this version, v2))
A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density --not by size-- the star can be much larger than Planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than Planckian by a factor (m/mP)n, where m is the mass fallen into the hole, mP is the Planck mass, and n is positive. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the 10−14cm wavelength.
Comments: 5 pages, 3 figures.

 

[Drakkith]

That's cool. Any idea what this "imprint" would look like?

 

[skydivephil]

This is really fascinatingy
We know of course black holes formed in the early universe, but is there enough time for a signal to get to us now?
IS this signal strong enough and/or unambiguous enough to be able to detect with current technology?
If we do detect it, I would think we are justified in assuming the big bang is replaced with a big bounce too, any reason why that would not be justified?

 

[D English]

If I understand the paper, the signals emitted by Planck Stars can be detected.

What I didn't gather was how big a star needs to be in order to be able to create a Planck star. Is it possible for a star to be big enough to create a black hole but not big enough to become a Planck Star? If yes, how big does a "pre-Planck" star need to be?

One of the things that blew my mind was how small a Planck Star would be (if I read it right). Sub atomic but still possessing Planck density.

Finally, and at risk of being nonsensical, if observers outside the Planck star effectively never see the bounce due to time dilation, are they still subject to the gravitational effects of the Planck Star while the bounce is frozen (but had already happened)? If I read it right, the bounce is nearly instantaneous, destroying the source of gravity (?) but outside the trapped zone the explosion takes a very long time to occur. Would this mean that an outside observer at risk of being pulled into the trapped zone would be subject to the gravitational pull until they enter the trapped region at which time they then are a part of a bounce that happened in the very distant past?

Gosh, it seems like time travel happens all the time in the cosmos.

 

[marcus]

If I understand the paper, the signals emitted by Planck Stars can be detected.

A Planck star is a proposed replacement for the BH "singularity". If you think of singularities as unphysical. Not occurring in nature, just failure points of a man-made theory. Then you wonder "what is REALLY there, instead of singularity where the theory breaks down?"

Loop cosmology says that instead of the cosmological singularity there is a bounce.
But after the bounce has happened and expansion has gotten under way, everything looks essentially the same, or almost the same, as in the classical cosmic model. The bounce can even help get inflation started.

This Planck star idea does the same thing for the BH singularity. Everything looks nearly the same for most of the time until the burst at the end. The Planck star is a STAND-IN for the singularity and it is surrounded by the same BH event horizon, and that BHEH radiates the same Hawking radiation.

Is it possible for a star to be big enough to create a black hole but not big enough to become a Planck Star?

No, in this theory collapsing to form a BH is the same thing as collapsing to form a Planck star.
It is just a different way to visualize the singularity instead of an infinitesimal mathematical point somehow containing infinite density and infinite curvature, you have a real macroscopic object undergoing a process that is normal according to LQG theory of how nature behaves, a bounce driven by quantum gravity corrections.

One of the things that blew my mind was how small a Planck Star would be (if I read it right). Sub atomic but still possessing Planck density...

A good way to get a handle on the SIZE of the Planck star at the center of a BH horizon is, I think, to look at Figure 1 and see how the INNER HORIZON is formed by the tilting back upright of the light cones.
The star, as I understand it, is just as big or as small as the region bounded by that inner horizon.

At the very instant the bounce occurs, the turnaround, that region is quite small as you point out. But still at least it is not zero-volume infinitesimal, not an abstract mathematical point.
Then after the turnaround it begins to expand, as the outer horizon shrinks down (due to loss of mass).
The critical point is when they coincide.

if observers outside the Planck star effectively never see the bounce due to time dilation, are they still subject to the gravitational effects of the Planck Star while the bounce is frozen (but had already happened)?

Clocks run slower deep in a gravity well. Outside the well, they run fast. From an outside perspective, timing with an outside clock, the bounce process could well take billions of years, so it will be billions of years before the explosion is visible.

From a close in perspective with a close-in clock whose internal parts run excruciatingly slowly, the bounce process happens in just a few ticks, very quickly.

Certainly the outside world is subject to the gravity effect of the Star mass during all those billions of years that the bounce takes to happen.

There is a long wait, with nothing but comparatively feeble Hawking radiation, and then a big bright flash. The time the flash occurs is when the inner region has swelled up (see Figure 2) to where it is no longer subject to such extreme time-dilation. Then things happen fast and there is a big star-burst.

Maybe I should wait and see if you put your question differently, or if this explanation works for you.

 

[D English]

I have to go. Don't have time to answer these last points, will get back.

I really appreciate your inputs. I changed the wording of the last sentence in the 2nd to last paragraph so that it made sense.

 

[D English]

Wow. Need to grok on this one. But off the top of my head, I intuitively think that when the explosion happens, time dilation is nullified because the density is no longer there.

Observationally, we see BHs at the center of galaxies that have been there for a long time.

 

[marcus]

...

Observationally, we see BHs at the center of galaxies that have been there for a long time.

Exactly. Rovelli and Vidotto show a calculation of the estimated lifetime and it is the same order of magnitude as the lifetime of a usual theoretical model BH evaporating as it emits Hawking radiation.
The Planck star version lifespan, as I recall, is about 60% of the lifespan of a usual theoretical model BH. The models are in many respects similar, in what they predict.

So what we see agrees with what R&V would say to expect, no stellar mass BH exploding around us. It is far far too early for that. And as for supermassive objects with lifetimes much longer than stellar mass. Forget it.

The calculated lifetime goes as the cube of the mass. To get a lifetime as short as 14 billion years (current time since beginning of expansion) you have to go to an absurdly UNmassive BH or Planck star. They estimate 10¹² kilogram. that is only a billion metric tons.
Figure, that would be a one kilometer size cube of something the density of water. The mass of an asteroid, not a star.

This in fact is the main obstacle to observation. The only way we could see evidence of Planck star explosion is if the early universe produced primordial black holes (i.e. primordial Planck stars) of a range of masses and sizes. And if some of these primordial objects were UNmassive enough that they have already evaporated down to critical size and exploded, during the 14 billion years since early universe days.

Somebody now has to calculate the cosmic ray spectrum that would result from a realistic range of primordial objects having been produced, much less massive than stars so that they could already have exploded and contributed to the cosmic ray background.
This is the KIND of calculation that has already been done for older model BH. R&V cite a couple of papers:

[34] D. Cline and W. Hong, “Possibility of Unique Detection of Primordial Black Hole Gamma-Ray Bursts,” ApJ 401 (1992) L60.

[35] D. B. Cline, S. Otwinowski, B. Czerny, and A. Janiuk, “Do Very Short Gamma Ray Bursts originate from Primordial Black Holes? Review,” http://arxiv.org/abs/1105.5363.

 

[marcus]

It's early days. I expect a paper with Matt Smerlak to come out that gets more precise about the relation between mass and lifetime. This would lead to greater precision in determining what imprint on the cosmic ray background there might be from EARLY LOW-MASS shorter lifetime objects exploding.
The paper in preparation with Smerlak is reference [25].

 

[D English]

Thought about it over the weekend.

I need help understanding part of it, but first I need to have some validation of my understanding and logic:

Understanding:
From the frame of the Planck Star, the bounce is instantaneous (the bounce "speed" is governed by the time c takes to cross the diameter of the object).

Logic:
When the bounce (aka explosion) occurs, the energy density of the Planck Star is dissipated to an extent that extreme time dilation is no longer in play.

Question:
If the explosion happens instantly, and the time-dilating energy density is dissipated, what keeps the observers seeing a time-dilated event?

EDIT: Argh- I think I just answered my own question... the time dilation happens at the moment of Planck density, not the bounce.

 

[marcus]

...
When the bounce (aka explosion) occurs,...

Part of this is just the words we use. I think of the "bounce" as a protracted process that only terminates with an explosion visible from the outside. One could also mean, by "bounce" the moment of highest density, the turnaround from contraction to expansion, which happens at the midpoint of the protracted process.

Either way I don't equate it with the visible explosion at the end. Some degree of time dilation is happening all the way along, until the very end when the object self-destructs and dissipates.

We are talking about something conceptually new, so we can't automatically rely on everybody using the words to mean the same thing. I think you and I UNDERSTAND and visualize it similarly, but are using different words, or using the same words differently. That will work itself out.

EDIT: ... the time dilation happens at the moment of Planck density, not the bounce.

I think you "get it" the same way I do, although we are using the word "bounce" with different meanings. In LQG the quantum effect that makes gravity repel instead of attract begins to kick in when density is about 1% of Planck and becomes more and more intense as density approaches Planck density.

So it slows down collapse and eventually stops it and then accelerates the re-expansion. For someone inside, it would seem to happen very quickly. For someone outside the whole thing might take 14 billion years. (Say for asteroid-size mass of billion metric tonnes.)

To illustrate with a rough approximate example, say collapse begins sometime in year zero. And the black hole temporary event horizon forms, and whatever is inside collapsed to where time dilation kicks in.

And then, by the outsiders clock, the actual moment of rebound (that I call the "bounce moment"), the moment of maximum density, maximum time dilation, maximum quantum effects repellency, happens at year 7 billion.

But for the temporary event horizon to shrink down a little (due to hawking radiation mass loss) and for inner object to swell out enough (following thru from the jolt of expansion it got) takes another 7 billion years.

So now we are at year 14 billion and the inner object has finally swelled up and bursts thru the event horizon, which is no longer, and time dilation is greatly diminished and now almost negligible. So the whole thing blows up.

That's how I would sketch an illustrative sample timetable. There are lots of details here I don't fully understand but that's my rough sketch.

In GR, according to the GR equation, geometry-change has a kind of "momentum" all its own. If some geometry starts expanding it is going to want to continue expanding although, at normal densities, the effect of matter will tend to slow it down. But it still has that geometric "momentum" from the initial kick-off and a tendency to continue.

 

[D English]

Thanks Marcus. The idea of "cumulative time dilation" makes a lot of sense to me.

I like your definition bounce too.

 

[marcus]

I'm glad it works for you D English!
What I want to do now is calculate how many of these primordial BH (if they account for the main bulk of dark matter) could be in our immediate neighborhood.

If you look down at the bottom of page 4 of the Rovelli Vidotto paper right before equation (23) you see where they calculate that the lifetime of a 10¹² kg primordial BH (planck star model) is roughly equal to the current time since start of expansion, in other words about 14 billion years.

So billion metric tons is the estimated LOWER LIMIT on primordial Planck star masses.

Any substantially lighter than that would have burst already and contributed to the gamma ray background.

Astronomers who estimate the dark matter density like to quote figures in GeV/cm³ which amounts to 1.8 x 10^-12 kg in a cubic kilometer.

Most estimates seem to be around 0.2 and 0.3 GeV/cm³ but one I saw was 1.3 plus or minus. So let's say it's 0.6 GeV/cm³
which would amount to 10^-12 kg in a cubic kilometer---a nice round number.

A quick way to do the conversion is to paste this into the google window:
0.6 GeV/cm^3/c^2*10^9 m^3
You can see 0.6 GeV/cm^3 as our benchmark density
and dividing by c^2 to get mass in kilograms
and multiplying 10^9 m^3 to get a cubic kilometer's worth.

So let's say we are interested in a primordial Planck star that is about the least massive that could still be around, namely 10¹² kg, also known as a billion metric tons, or modest asteroid mass. One of those in a volume 10²⁴ cubic kilometers would come out to be the benchmark density.

Allowing for there being a range of masses all LARGER than the benchmark would make the number density lower, you'd have fewer bigger packages. So a rough upper estimate of the NUMBER density in the solar system neighborhood is ONE Planck star in a cube that is 100 million km on a side.

You know the radius of Earth orbits about 150 million km. So that cube is somewhat less than an AU on a side. Visually it is a large chunk of the inner solar system.

My understanding is that since these things are extremely tiny they almost never COLLIDE with any thing, they are very sparsely distributed in the first place but even if they were to pass thru the Earth it probably wouldn't slow them down.

If someone wants they can calculate the Schwarzschild BH RADIUS for a 10¹² kg mass. 2GM/c² It's really really tiny.

However the temporary exposure to the thing's gravity, as it passed through, might do some damage. Maybe it's a good thing that primordials (if they exist0 are sparsely sparsely distributed.

 

[marcus]

It is interesting that the concentration of DM is so much higher in our galaxy than it is on average in the universe overall.

Estimates of the DM density in the solar system neighborhood vary but using a benchmark of 0.6 GeV/cm³ I got that a 100 million km cube would contain a billion metric tons.

On the other hand the overall average DM density is estimated to be roughly a MILLIONTH of that! In energy equivalent it is about 0.2 joule per cubic kilometer. So our big cube would contain
0.2 x 10²⁴ joules/c² of mass

Using google calculator:
.2e24 joule/c^2 = 2225300.11 kilograms

Only around two thousand metric tons!

So that test cube whose side is the orbit radius of Venus, hence roughly on a scale with the inner solar system, would if it were put way out in intergalactic space have only 2225 tons of dark matter. But here in our galaxy, where dark matter is gathered, the same cube would contain 1000 000 000 tons.

A factor of almost half a million. Unless I've made an error that represents a radical amount of clumping. We know that DM gathers in clouds and surrounds galaxies and groups of galaxies. We think it has collapsed into wispy cobwebby structures which formed the framework on which ordinary matter has condensed. Still I was surprised by how much more than average concentrated it is in-and-around our galaxy.