Are Black Holes Hollow?

[Guest Phoenix_Enflame]

Hi Phoenix, Re push/pull

 

My guess is particles are both pushed and pulled as they pass through the acceleration tube. Sort of like an ordinary electric motor. The reason I used the word 'believe' is I have not gotten a response yet from the Fermilab forum. I simply asked if mass is created during the acceleration prossess.

 

I assume it is because people are always discussing the mass of these particles in mega and giga volts, and those seem to be associated SI units of mass. Could be wrong. However, these particles are accelerated to very near the speed of light. Well in excess of 99.999 percent. And yet they are in no way near infinite mass that would be required if they actually attained the speed of light.

 

I would really really like to see a graph plotting the mass change from motionless to the speed of light itself using one gram of matter to start. Given the very high speeds attained in a 'simple' particle accelerator, it seems to me space travel at very high speeds might not require the amount of energy I once suspected.

 

Hello again,

I am very interested to know what you will find with your push/pull theory.

Originally, when I first read about the accelerators, I had assumed that the magnets forced the particles around the accelerator. I even used the analogy of toothpaste being squeezed through the tube, to my son (10).

However, after visiting a children's museum here, we saw a model collider and the magnets actually pulled the particle around. In this particular model anyway.

Anyway, just thought I would share.

[Guest Phoenix_Enflame]

More Rambling

 

Matter speeding towards the final qubic plank would need to come to a very sudden stop upon entering the area. A nifty singularity might seem a good solution, but it is not. This is because Black Holes grow, as do their event horizons. A singularity seems obligated to gobble up all of it, but does not.

 

The more elegant solution to this problem is TIME comes to a very sudden strop PRIOR to matter passing the final plank unit. Hence, the BH would be hollow?

 

I actually really like this theory.

[CraigD]

By way of topic introduction, one TV reader said we would be 'spaghettified' falling into a BH.

When science popularizers speak of ”spaghettification” in the context of black holes, they’re referring to the difference in acceleration of gravity of parts of a single body at different distances from the black hole – know as tidal force - becoming so great that it tears the body apart. The allusion to a human body being pulled thin like spaghetti is a polite fiction – in reality, such an effect would be as ugly and messy as dismembering a human body with a powerful pulling machine. This popular bit of tack appears to be due to the ever polite Steven Hawking, appearing in his famous 1988 book “A Brief History of Time”.

 

Assuming a long body with most of its mass in its ends, tidal force is given by [math]F = u m \left( \frac1{r^2} - \frac1{(r+l)^2} \right)[/math], where [math]u[/math] is the standard gravitational parameter ([math]G M[/math]) of the primary body, [math]m[/math] the mass of each end of the body, [math]l[/math] the length of the body, and [math]r[/math] the distance between the body and the primary body. The effect is observed by objects falling toward and orbiting nearly any body – for example unstabilized artificial satellites tend to orient themselves with their long axes pointing toward the Earth. For [math]m = 50 \,\mbox{kg}[/math] and [math]l = 1 \,\mbox{m}[/math], a rough representation of a human body, in a typical low Earth orbit , [math]F \dot= 10^{-4} \,\mbox{N}[/math].

 

In the post ”Some startling (to me) black hole calculation results”, I showed results of this and related calculations for black holes of different masses, some believe possible, some not. The key thing such calculations show is that a black hole with a mass of several hundred thousand stars has very slight, non-injurious tidal forces all the way down to its event horizon (though there are plenty of other things to kill you around all known black holes, mainly their hot, intensely radiant accretion disks). Also, as the size of a black hole increases, the average density of the volume within its event horizon decreases. This suggests that a very large black hole could consist of a collection of ordinary galaxies/clusters of galaxies, and has lead to serious speculation that parts of or the entire visible universe may, to an observer outside these volumes, actually be black holes.

Our base team on the outside would notice we BH travelors would have become microscopically thin and our time come to a virtual halt.

Although it is, I think, a correct interpretation of general relativity that a distant observer (our base team) sees the BH travelers move slower and slower, nearly freezing altogether near and never quite reaching the event horizon, it does not predict that they become thinner. Although special relativity predicts both time dilation and length contraction, GR predicts only time contraction.

Anyway, as we fall into the BH we would notice the Plank distance did not changed at all.

As noted above, length contraction doesn’t occur due to GR gravitational fields, contradicting this claim. However, this claim is commonly made concerning SR, and is a very interesting, and much discussed. Troublingly, it strongly contradicts the special relativity principle of the non-existence of preferred frames, because one could in principle measure the Planck length in laboratories with different relative velocities and in different directions, and determine the “true rest frame”. In 2001, a fairly well known, but by no means widely accepted, response to this appeared, a modification of special relativity known as doubly-special relativity.

I assume it is because people are always discussing the mass of these particles in mega and giga volts, and those seem to be associated SI units of mass.

For convenience, the rest and relativistic mass is commonly expressed in units of electron volts (eV, MeV, GeV, etc.). This is a slight misnomer – the eV is actually a unit of energy. The related unit of mass is [math]\frac{\mbox{eV}}{c^2}[/math]. Because “electron volt divided by the speed of light in vacuum squared” is awkward to say or write, the unit is conventionally shortened to just “electron volt”.

However, these particles are accelerated to very near the speed of light. Well in excess of 99.999 percent. And yet they are in no way near infinite mass that would be required if they actually attained the speed of light.

 

I would really really like to see a graph plotting the mass change from motionless to the speed of light itself using one gram of matter to start.

The formula for mass dilation is [math]m = \frac{m_0}{1- \left( \frac{v}{c} \right)^2}[/math]. With this, it’s easy to calculate the mass of a particle at any relative speed. For example, the mass of a 1 gram body traveling 99.999 c is [math]\frac{0.001 \,\mbox{kg}}{1- 0.99999^2} \dot= 0.224 \,\mbox{kg}[/math]. It’s easy to plot with a graphing calculator, or a website such as this one, giving a graph like this:

Given the very high speeds attained in a 'simple' particle accelerator, it seems to me space travel at very high speeds might not require the amount of energy I once suspected.

Via particle accelerators, mass dilation has been confirmed with great certainty, so it’s very unlikely that it doesn’t also apply to spacecraft. Other factors, particularly that interstellar space is far from a perfect vacuum, so that a ship traveling at very high speed would experience a lot of heating due to friction, present daunting challenges to flying spacecraft even at speeds where mass dilation remains negligible.

 

 

To get to the main point of this thread

If everything that falls into a BH comes to a screaching time stop approaching the center, then the center is empty. Hollow...

Litespeed’s reasoning is indeed consistent with relativity. However, it supposes that black holes form by matter falling into them from outside their event horizons. Stellar mass black holes are believed to form when stars become so compact that their radii is less than the radius of their event horizon. In other words, their event horizons appear due to changes in the arrangement of their mass within that radius, not be anything that occurs outside of their event horizon.

 

Supermassive black holes such as those believed to lie at the cores of all or most galaxies are believed to have accreted from many smaller black holes, and in some cases, two or more supermassive black holes combining. How this can occur in a way consistent with relativity is an interesting, but not intractable problem, which is left as an exercise for the reader. :)

[litespeed]

Craig - Really Helpfull post

 

I figured a 'mass dialation chart' would be of the hocky-stick type, thus leading me to suppose reasonable amounts of energy would be able to increase velocity to very high levels relative to light. It had not occured to me 'stuff' would be in the way during the trip!

 

Your discussion of the original creation of a black hole is interesting to me. You wrote: "Stellar mass black holes are believed to form when stars become so compact that their radii is less than the radius of their event horizon. In other words, their event horizons appear due to changes in the arrangement of their mass within that radius, not be anything that occurs outside of their event horizon."

 

This does not seem inconsistent with a hollow black hole. Specifically, it seems to me there are plenty of empty 'plank volumes' about which their mass might be rearanged. One thing you might help me with is 'how much mass can fit into one plank volume'. If, in fact, there is such a unit in theoretical physics!

 

If there is such a unit, and if there is a limit, then black holes could be solid; the last unit having been filled to capacity. This seems counter intuitive to me because it seems to imply time in that last unit volume would be absolutely stopped. This to account for momentum conserved as mass jumped into that last unit. If there is no limit, then at least one singularity seems inevitable. A hollow black hole seems to this novice to be as plausible as these possibilities.

 

I realize I am simply spouting theories based upon VERY LIMITED education in this area. However, by postulating them I encourage others to make corrections and explanations. Thanks for the attention!

[CraigD]

This does not seem inconsistent with a hollow black hole.

I don’t think any theory suggests that black holes are uniformly filled within their event horizons, so describing them as “partly hollow” is consistent with best theory.

 

Black holes involve an important scaling relationship. The radius of their event horizon, AKA the Schwarzschild radius of a body with mass [math]M[/math], is

 

[math]r_s = k_1 M[/math], where [math]k_1 = \frac{2G}{c^2}[/math]

 

Geometrically, radius is related to volume (of a sphere) [math]V[/math] by

 

[math]r = k_2 V^{\frac13}[/math], where [math]k_2 = \left( \frac{3}{4 \pi} \right)^{\frac13}[/math]

 

So the average density ([math]\frac{M}{V}[/math]) of the volume within the event horizon of a black hole can be very low, if its mass is very high. For a black hole of about 130 million (130000000) solar masses ([math]3 \times 10^{38} \,\mbox{kg}[/math], this average density is about the same as water ([math]1000 \,\mbox{kg/m}^3[/math]). For one of about 1 billion ([math]10^9[/math]) solar masses, it’s about the same as air at sea level ([math]1 \,\mbox{kg/m}^3[/math]). For a black hole the mass of the observable universe, depending on assumptions about the ratio of visible to invisible (“dark”) matter, its average density is between [math]8 \times 10^{-26}[/math] and [math]2 \times 10^{-28} \,\mbox{kg/m}^3[/math], a range that spans, with the same assumptions about dark matter, the actual density of the observed universe.

 

Specifically, it seems to me there are plenty of empty 'plank volumes' about which their mass might be rearanged. One thing you might help me with is 'how much mass can fit into one plank volume'. If, in fact, there is such a unit in theoretical physics!

The Planck length (about [math]1.6 \times 10^{-35} \,\mbox{m}[/math]), isn’t the length of the side of a smallest volume into which anything can go, but rather related to the theoretical limit of the smallest distance that can be measured. Distances can be in arbitrarily smaller units that the Planck length, we just can’t, in principle, ever physically measure such small differences.

 

How much mass can exist within a particular volume depends on what kind of particle carries the mass. Fermions, the usual particles we think of as having mass, usually obey rules that, roughly stated prohibits them from “occupying the same volume” on a scale of about [math]10^{20}[/math] Planck lengths. Bosons don’t obey these rules, so an unlimited number of them can occupy the same volume. Bosons that we think of as having mass (for example, gluons, which make up most of the mass of protons and neutrons), however, follow complicated rules confining them to the close vicinity of fermions, so their “unlimited density” quality can’t be realized straightforwardly.

 

Worse there’s no well accepted theory describing gravity in terms of fermions and bosons, so no firm theoretical predictions of how they behave in very high gravity fields such as around and within the event horizon of a stellar mass black hole. There’re books full of interesting speculation, but the best of them focus mostly on how little we know about gravity on this scale.

 

Based on firm theory and observational evidence of black holes from a few solar masses to supermassive ([math]10^5[/math] to [math]10^{10}[/math] solar, however, it’s pretty safe to say that black holes don’t have a maximum capacity.

[Moontanman]

 

In the post ”Some startling (to me) black hole calculation results”, I showed results of this and related calculations for black holes of different masses, some believe possible, some not. The key thing such calculations show is that a black hole with a mass of several hundred thousand stars has very slight, non-injurious tidal forces all the way down to its event horizon (though there are plenty of other things to kill you around all known black holes, mainly their hot, intensely radiant accretion disks). Also, as the size of a black hole increases, the average density of the volume within its event horizon decreases. This suggests that a very large black hole could consist of a collection of ordinary galaxies/clusters of galaxies, and has lead to serious speculation that parts of or the entire visible universe may, to an observer outside these volumes, actually be black holes.

 

This is an interesting idea, would this mean that inside the galaxies that are inside a black hole there could be black holes? This would even suggest that there might be black holes inside the black holes inside the galaxies inside the black holes. I'm not sure but this looks like a possible infinite series of black holes always smaller and smaller?

[CraigD]

This is an interesting idea, would this mean that inside the galaxies that are inside a black hole there could be black holes?

I know of no reason why not

This would even suggest that there might be black holes inside the black holes inside the galaxies inside the black holes. I'm not sure but this looks like a possible infinite series of black holes always smaller and smaller?

If, as most theorists believe, Hawking radiation occurs, there’s a limit to how small a black hole can exist (for more than a very short duration), so there’s a limit to how deep the nesting can be. Assuming the observable universe is itself a black hole (by no means a sure assumption), there could be nesting in the outward direction, beyond the radius of the observable universe, though this sort of thinking gets tangled in deep questions about the origin of the universe and the nature of gravity.

 

I strongly suspect the regions within the event horizons of center-of-galaxy supermassive ([math]10^5[/math] to [math]10^{10}[/math] solar mass) black holes contain black holes of various masses, involved in a complicated dynamic in which their event horizons change and shift as central masses rearrange. Although, being theoretically impervious to observing with light, space probes, etc, there’s no obvious way to confirm this, if general relativity’s predictions about gravitational waves are correct, it should be possible to measure with gravitational wave detectors. Also, if this theory is correct, the dynamic can gain (as the black hole grows) and lose (as it slightly shrinks) energy.

 

I’ve not made even rough calculations around these speculations, so can’t estimate much about this dynamic, such as predicting whether galactic centers are strong gravity wave emitters for a long time, or only shortly after their formation or accretion with other galaxy’s. My speculation could, of course, be entirely wrong, either due to some basic misunderstanding of theory on my part, or due to a lack of basic theory of the nature of gravity to understand. In modern physics, gravity is subject area full of unanswered questions, nearly as many or more now than thirty years ago. It’s proving to be a big, tough question.

[Pluto]

G'day from the land of ozzzzzz

 

I have read that the max for a black hole is 50 billion sun masses.

 

I trying to find the info

 

Here is a link on a 18 Billion sun mass

 

18 Billion Suns -A Galaxy Classic: Biggest Black Hole in Universe Discovered?and it?s BIG

 

Now the mechanism that stops the so called black hole from becoming larger goes beyond the Steven Hawking evaporatiion.

 

I would assume that the transition between phases of degerate matter would play a critical part.

[modest]

It might be interesting to note that Birkhoff's theorem holds in the case of a Schwarzschild black hole. This would mean the gravitational field outside the event horizon of a black hole would be the same if it contains a singularity or any other spherically symmetric distribution of mass such as a spherical shell.

 

In other words, there would be no way to tell from outside the black hole (assuming it has no charge or angular momentum) if it has a singularity or is hollow.

 

~modest

[Pluto]

G'day

 

Early I said I had links on the size of Black holes.

 

Upper Limits on the Mass of Supermassive Black Holes from Archival Data of the Space Telescope Imaging Spectrograph

 

Upper Limits on the Mass of Supermassive Black Holes from Archival Data of the S

Oct-08

 

The growth of supermassive black holes (SBHs) appears to be closely linked with the formation of spheroids. There is a pressing need to acquire better statistics on SBH masses, since the existing samples are preferentially weighted toward early-type galaxies with very massive SBHs. With this motivation we started a project aimed at measuring upper limits on the mass of the SBHs that can be present in the center of all the nearby galaxies (D<100 Mpc) for which STIS/G750M spectra are available in the HST archive. These upper limits will be derived by modeling the central emission-line widths ([N II] λλ 6548,6583Å, Hα, and [s II] λλ 6716,6731Å) observed over an aperture of ˜0.1 arcsec (R<50 pc).

 

and

 

Upper Limits on the Masses of 105 Supermassive Black Holes from HST/STIS Archival Data

Upper Limits on the Masses of 105 Supermassive Black Holes from HST/STIS Archiva

[maddog]

Early I said I had links on the size of Black holes.

 

Upper Limits on the Mass of Supermassive Black Holes from Archival Data of the Space Telescope Imaging Spectrograph

Upper Limits on the Mass of Supermassive Black Holes from Archival Data of the S Oct-08

 

&

 

Upper Limits on the Masses of 105 Supermassive Black Holes from HST/STIS Archival Data

Upper Limits on the Masses of 105 Supermassive Black Holes from HST/STIS Archiva

First article to have/read costs $ (Annoying).

From 2nd article I see this is a sampling of the nearest galaxies.

So in essence a "Upper Limit" being discussed is what the Upper Limit is for the representative sample.

 

This is in contrast to considering what an upper limit in theory to what a Black Hole (BH) can be.

 

I think that would be fundamental to consider whether BHs could be "hollow".

 

maddog

[CraigD]

Good research, Pluto! :thumbs_up

 

However, from it’s abstract, Beifiori et al's paper appears to be a survey of astronomical spectroscopy data placing an upper limit on the largest black hole that has formed in the center of any galaxy, not an upper limit on how large a galactic center or other black hole may eventually form.

 

I think the quote from “18 Billion Suns -A Galaxy Classic: Biggest Black Hole in Universe Discovered?and it?s BIG” from post #25 states the theoretical consensus:

So just how big can these bad boys get? Craig Wheeler of the University of Texas in Austin, US, says it depends only on how long a black hole has been around and how fast it has swallowed matter in order to grow. "There is no theoretical upper limit," he says.

So your suggestion

Now the mechanism that stops the so called black hole from becoming larger goes beyond the Steven Hawking evaporatiion.

 

I would assume that the transition between phases of degerate matter would play a critical part.

Seems to me unsupported. There appears to be no basic physical law limiting the maximum size of a black hole. Rather, the limit appears to be related to how much time a super-massive black hole has had to accrete additional matter, especially other black holes and SBHs.

 

It’s important to understand that, counterintuitively, Hawking radiation power P is inversely proportional to the mass of a black hole M ([math]P = \frac{K}{M}[/math], where [math]K[/math] is a constant), so the larger a black hole, the less its rate of mass loss due to Hawking radiation. Therefore, this theory places a lower limit on the mass of a black hole.

 

Assuming it’s only source of infalling matter/energy is cosmic background radiation, a black hole smaller than about [math]4 \times 10^{22} \,\mbox{kg}[/math] (about the mass of the moon) would lose mass, while one larger would gain mass. The predicted lifetime of a black hole is about [math]M^3 \cdot 8.415 \times 10^{-17} \,\mbox{s/kg}^3[/math], so, for example, a black hole the mass of a fully fueled Space Shuttle would last about 11 minutes (673 s).

I would assume that the transition between phases of degerate matter would play a critical part.

Again counterintuitively, the structure of the matter in a black hole is predicted by best accepted theory to have little to do with its theoretical maximum or minimum size. Hawking radiation, for example, is actually an effect due to the space just outside of the black hole and the black hole’s gravity, not the space or matter within the black hole.

 

For a star-mass body to be dense enough to be contained within its event horizon, and thus be a black hole, its matter must be degenerate. For a hypothetical black hole much larger, its density could in principle be much smaller. For example, a black hole of about 40,000,000 solar masses would have the average density of water (though such a mass being kept at a uniform density against the force of its own gravity is a separate question).

[CraigD]

It might be interesting to note that Birkhoff's theorem holds in the case of a Schwarzschild black hole. This would mean the gravitational field outside the event horizon of a black hole would be the same if it contains a singularity or any other spherically symmetric distribution of mass such as a spherical shell.

 

In other words, there would be no way to tell from outside the black hole (assuming it has no charge or angular momentum) if it has a singularity or is hollow.

I agree.

 

However, since Birkhoff’s theorem and other similar “no hair” rules explicitly apply to spherically symmetrical bodies only. General relativity predicts that a body that emits gravitational waves cannot be spherically symmetrical, either.

 

Therefore, I don’t think any of these theories contradict the suggestion that a black hole can emit gravitational waves, provided that its mass/energy is not arranged spherically symmetrically. What I suggest in post #24 is that black holes formed by the accretion of massive bodies such as other black holes are not spherically symmetrically, and thus should be expected to emit gravitational waves, providing some information about the structure within their event horizons.

 

I’ve still not done the calculations to make even a rough approximate prediction. We know from present-day gravity wave detectors’ failure to directly detect any gravity waves that the effect can’t be enormous, though. I find the prospect exciting, however, because it suggest that some day, gravity wave observations may allow a sort of “black hole archeology” that may allow detailed histories of the formation of SBHs to be determined, which in turn could tell a lot about the histories of their surrounding galaxies.

[Pluto]

G'day

 

CraigD said

 

For example, a black hole of about 40,000,000 solar masses would have the average density of water (though such a mass being kept at a uniform density against the force of its own gravity is a separate question).

 

Please supply papers to support this.

[modest]

However, since Birkhoff’s theorem and other similar “no hair” rules explicitly apply to spherically symmetrical bodies only...

 

Therefore, I don’t think any of these theories contradict the suggestion that a black hole can emit gravitational waves, provided that its mass/energy is not arranged spherically symmetrically. What I suggest in post #24 is that black holes formed by the accretion of massive bodies such as other black holes are not spherically symmetrically, and thus should be expected to emit gravitational waves, providing some information about the structure within their event horizons.

 

Looking again at my previous post it appears as if I'm responding to your suggestion in post 24, which was not at all my intention.

 

I tentatively agree with both your speculation that the interior might have prolonged and complicated interactions and that such a thing should be observable via gravitational waves.

 

The only complication that comes up in my mind is the speed of propagation of a gravitational wave. While I'm sure the speed is supposed to be c, I'm not sure what that should mean in the case of a black hole. My uninformed intuition says that a gravitational wave should escape an event horizon, but that same intuition fails me in the case of the electromagnetic field.

 

Information about charge is allowed to leave the hole while waves in that same field are not. I don't understand the distinction, but I suppose it's possible that the same situation would present itself in the case of gravity such that information about the mass behind the horizon could escape, but waves (perhaps quantized) could not.

 

I'm just thinking out loud here and I have a strong suspicion the physics involved is beyond me. :)

 

~modest

[Pluto]

G'day Modest

 

You spoke of Electromagnetic fields, smile I just finished reading this link. I hope its of interest to you. If not,,,,,,,oh well.

 

The Electrodynamics of the Core and the Crust components in Neutron Stars

The Electrodynamics of the Core and the Crust components in Neutron Stars

Oct-08

 

 

We study the possibility of having a strong electric field (E) in Neutron Stars. We consider a system composed by a core of degenerate relativistic electrons, protons and neutrons, surrounded by an oppositely charged leptonic component and show that at the core surface it is possible to have values of E of the order of the critical value for electron-positron pair creation, depending on the mass density of the system. We also describe Neutron Stars in general relativity, considering a system composed by the core and an additional component: a crust of white dwarf-like material. We study the characteristics of the crust, in particular we calculate its mass Mcrust. We propose that, when the mass density of the star increases, the core undergoes the process of gravitational collapse to a black hole, leaving the crust as a remnant; we compare Mcrust with the mass of the baryonic remnant considered in the fireshell model of GRBs and find that their values are compatible.

 

=================

 

As for hollow black holes.

 

The only part that seems to be hollow is the vortex that is coming out or seems to from the core.

 

 

As for the density of the core

 

Normal matter can reach 10^5 kg/m3

Neutron matter 10^17 Kg/m3

Theoretical quark composites from 10^18 to about 10^ 25 Kg/m3

Theoretical Neutrino/Preon particles matter upto about 10^35 Kg/m3 This is getting close to what a singularity is.

 

There are various degrees of compact matter and there a mimickers of blackholes.

 

That reminds me I should have a link on mimickers.

 

 

As for the physics side of it,,,,,,,I'm with Modest.

[CraigD]

G'day

 

CraigD said

For example, a black hole of about 40,000,000 solar masses would have the average density of water (though such a mass being kept at a uniform density against the force of its own gravity is a separate question).

Please supply papers to support this.

Although I’ve read several popular science articles that suggested calculations such as the above, my own posts at hypography, such as this one, are the only writing of which I’m aware that presents them in table form for various orders of magnitude of mass. I can provide sources only for the underlying equations, not my particular use of them.

 

The claim follows directly from the equation for Schwarzschild radius,

 

[math]r_s = \frac{2Gm}{c^2}[/math]

 

for the volume of a sphere,

 

[math]V = \frac43 \pi r^3[/math]

 

and the definition of density

 

[math]p = \frac{m}{V}[/math]

 

A black hole with a mass of [math]2.6 \times 10^{38} \,\mbox{kg}[/math] has a Schwarzschild radius [math]2 \cdot 6.67428 \times 10^{-11} \cdot 2.6 \times 10^{38} / 299792458^2 = 3.86159 \times 10^{11} \,\mbox{m}[/math]. The volume of a sphere of this radius is [math]4 / 3 \cdot 3.14159 \cdot (3.86159 \times 10^{11})^3 = 2.41206 \times 10^{35} \,\mbox{m}^3[/math]. So the average density of the matter within the event horizon of this back hole is [math]2.6 \times 10^{38} \cdot 2.41206 \times 10^{35} = 1.07791 \,\mbox{kg/m}^3[/math], only a bit more than fresh water ([math]1 \,\mbox{kg/m}^3[/math]) or seawater (about [math]1.029 \,\mbox{kg/m}^3[/math]).

 

Note that, as I noted parenthetically above, a low average density of a black hole doesn’t imply that it doesn’t actually consist of regions of very high and very low density. I strongly suspect the internal structure of greater than stellar mass black holes is very complicated.