BHs, the fuzzball versus wormhole debate

[notFritzArgelander]

https://phys.org/news/2022-01-black-hol ... ebate.html

The reported work claims to solve the Hawking information paradox by assuming that string theory is correct. BHs are fuzzballs of strings with the mass NOT concentrated centrally. But this is not an empirical test just a mathematical proof that assumes string theory as a basis for calculation.

However, the result has implications for ECSK gravity theories which prefer wormhole solutions as a resolution of the information paradox. Since empirical evidence is not available, there is no need to abandon ECSK yet. However the result would seem to show that string theory plus General Relativity has irreconcilable differences with ECSK.

I'll probe more later.

[turboscrew]

I wonder, how such a whole BH filling fuzzball keeps together?

[notFritzArgelander]

I wonder, how such a whole BH filling fuzzball keeps together?

Gravity, as in GR is adequate. The fuzzies made of strings have mass. So this is really about the mass distribution inside the BH. If the work is good, it would say that string theory implies that the mass cannot be concentrated in a point singularity at the center. So this can really be appreciated as another blow to the mass point singularity of classical GR. Nature eschews singularities.

[pakarinen]

Although I consider string theory to be a fuzzball of craziness, this could be interesting.

[notFritzArgelander]

Although I consider string theory to be a fuzzball of craziness, this could be interesting.

I plan to read the paper and report since the implications are largish .

[Michael131313]

Thanks nFA. Interesting article. I am looking forward eagerly for your report.

[notFritzArgelander]

The link in the article goes to a paywalled paper. Fortunately arXiv comes to rescue us.

https://arxiv.org/abs/2105.06963

The quantum gravity vacuum must contain virtual fluctuations of black hole microstates. These extended-size fluctuations get `crushed' when a closed trapped surface forms, and turn into on-shell `fuzzball' states that resolve the information puzzle. We argue that these same fluctuations can get `stretched' by the anti-trapped surfaces in an expanding cosmology, and that this stretching generates vacuum energy. The stretching happen when the Hubble deceleration reduces quickly, which happens whenever the pressure drops quickly. We thus get an inflation-scale vacuum energy when the heavy GUTS particles become nonrelativistic, and again a small vacuum energy when the radiation phase turns to dust. The expansion law in the radiation phase does not allow stretching, in agreement with the observed irrelevance of vacuum energy in that phase. The extra energy induced when the radiation phase changes to dust may explain the tension in the Hubble constant between low and high redshift data.

Translation with parenthetical thoughts: Quantum gravity must have vacuums that contain virtual black holes. These finite size micro states are squeezed when an event horizon forms and become energy conserving fuzzball states. The fluctuations can get stretched with the expanding universe and this generates a vacuum energy. (Dark energy perhaps?) When the Hubble deceleration drops with the drop in pressure one gets an energy sufficient to drive inflation when the particles of a Grand Unified Theory become non relativistic. (When the temperature drops below their rest energy.) When the universe is radiation dominated stretching is disallowed. At the transition from radiation to matter dominated pressure might explain the tension in the Hubble constant.

Apart from the incidental mention of fuzzballs this appears to be a completely different research result! It is less about the BHs and more about cosmology. ?????

So I looked for more references on arXiv and found

The fuzzball proposal for black holes: an elementary review

https://arxiv.org/abs/hep-th/0502050

We give an elementary review of black holes in string theory. We discuss BPS holes, the microscopic computation of entropy and the `fuzzball' picture of the black hole interior suggested by microstates of the 2-charge system.

This seems to be something more like what the article claimed to represent but its the OTHER article that is linked.

I guess I have 2 things to read now....

[Michael131313]

Thanks very much nFA. When I read the excerpt I too wondered when they would get to BHs.

[notFritzArgelander]

Thanks very much nFA. When I read the excerpt I too wondered when they would get to BHs.

More to come.....

[turboscrew]

I wonder what this means?

"The black hole tries to squeeze things to a point, but then the particles get stretched into these strings, and the strings start to stretch and expand and it becomes this fuzzball that expands to fill up the entirety of the black hole."

To my understanding, the size of a black hole is usually taken to be the volume within the event horizon.
In that case, most BHs are less dense than gas clouds.
How does it, then, keep being a BH?

[notFritzArgelander]

I wonder what this means?

"The black hole tries to squeeze things to a point, but then the particles get stretched into these strings, and the strings start to stretch and expand and it becomes this fuzzball that expands to fill up the entirety of the black hole."

To my understanding, the size of a black hole is usually taken to be the volume within the event horizon.
In that case, most BHs are less dense than gas clouds.
How does it, then, keep being a BH?

This is an interesting point that puzzles folks at first. The criterion for being a (non rotating spherical BH) is that an event horizon exists at a radius from the central mass r(Schwarzschild) = 2GM/c^2 with 2 being the set containing the set that contains the empty set (can't resist making a punlike reference to a recent thread, sorry, ) G the gravitational constant M the mass and c^2 the square of the speed of light.

But the density is estimated as being ρ = M/Volume = (and once you fiddle the algebra you get an expression) ~ 1/M^2.

So density isn't the criterion for having a BH. All you have to do is accumulate enough mass-energy to fill a certain volume. The density becomes arbitrarily low as the mass gets arbitrarily high.

[turboscrew]

I wonder what this means?

"The black hole tries to squeeze things to a point, but then the particles get stretched into these strings, and the strings start to stretch and expand and it becomes this fuzzball that expands to fill up the entirety of the black hole."

To my understanding, the size of a black hole is usually taken to be the volume within the event horizon.
In that case, most BHs are less dense than gas clouds.
How does it, then, keep being a BH?

This is an interesting point that puzzles folks at first. The criterion for being a (non rotating spherical BH) is that an event horizon exists at a radius from the central mass r(Schwarzschild) = 2GM/c^2 with 2 being the set containing the set that contains the empty set (can't resist making a punlike reference to a recent thread, sorry, ) G the gravitational constant M the mass and c^2 the square of the speed of light.

But the density is estimated as being ρ = M/Volume = (and once you fiddle the algebra you get an expression) ~ 1/M^2.

So density isn't the criterion for having a BH. All you have to do is accumulate enough mass-energy to fill a certain volume. The density becomes arbitrarily low as the mass gets arbitrarily high.

I'm thinking that, neutron star keeps being a neutron star, because the gravitation of the "halves" make very high pressure in the middle. So much mass so near. I'd think if the density becomes low, the "edges" of the mass are far, and the gravitational pull of the other half becomes much smaller. Or why is it, that a star can become a black hole even if it looses mass (SNR)?

[notFritzArgelander]

I wonder what this means?


To my understanding, the size of a black hole is usually taken to be the volume within the event horizon.
In that case, most BHs are less dense than gas clouds.
How does it, then, keep being a BH?

This is an interesting point that puzzles folks at first. The criterion for being a (non rotating spherical BH) is that an event horizon exists at a radius from the central mass r(Schwarzschild) = 2GM/c^2 with 2 being the set containing the set that contains the empty set (can't resist making a punlike reference to a recent thread, sorry, ) G the gravitational constant M the mass and c^2 the square of the speed of light.

But the density is estimated as being ρ = M/Volume = (and once you fiddle the algebra you get an expression) ~ 1/M^2.

So density isn't the criterion for having a BH. All you have to do is accumulate enough mass-energy to fill a certain volume. The density becomes arbitrarily low as the mass gets arbitrarily high.

I'm thinking that, neutron star keeps being a neutron star, because the gravitation of the "halves" make very high pressure in the middle. So much mass so near. I'd think if the density becomes low, the "edges" of the mass are far, and the gravitational pull of the other half becomes much smaller. Or why is it, that a star can become a black hole even if it looses mass (SNR)?

Understood. But here the informal model you've constructed is misleading you a bit about BHs although it works for neutron stars. I remember being surprised in the same way when I was doing homework problems in GR 50 years ago. One was, compute the Schwarzschild radius that corresponds to the density of water. NSs and BHs are very different and the model of "gravity holding it together" works for the NS but fails for the BH. A BH forms only when an event horizon forms and the criterion for that is "does the mass inside this radius equal the Schwarzschild radius."

A SN makes a BH because an explosion compresses the core while the blast wave ejects the envelope. The core is pushed in by the failure of pressure support while the shock wave powered by nucleosynthesis in the outer regions ejects the envelope.

[turboscrew]

This is an interesting point that puzzles folks at first. The criterion for being a (non rotating spherical BH) is that an event horizon exists at a radius from the central mass r(Schwarzschild) = 2GM/c^2 with 2 being the set containing the set that contains the empty set (can't resist making a punlike reference to a recent thread, sorry, ) G the gravitational constant M the mass and c^2 the square of the speed of light.

But the density is estimated as being ρ = M/Volume = (and once you fiddle the algebra you get an expression) ~ 1/M^2.

So density isn't the criterion for having a BH. All you have to do is accumulate enough mass-energy to fill a certain volume. The density becomes arbitrarily low as the mass gets arbitrarily high.

I'm thinking that, neutron star keeps being a neutron star, because the gravitation of the "halves" make very high pressure in the middle. So much mass so near. I'd think if the density becomes low, the "edges" of the mass are far, and the gravitational pull of the other half becomes much smaller. Or why is it, that a star can become a black hole even if it looses mass (SNR)?

Understood. But here the informal model you've constructed is misleading you a bit about BHs although it works for neutron stars. I remember being surprised in the same way when I was doing homework problems in GR 50 years ago. One was, compute the Schwarzschild radius that corresponds to the density of water. NSs and BHs are very different and the model of "gravity holding it together" works for the NS but fails for the BH. A BH forms only when an event horizon forms and the criterion for that is "does the mass inside this radius equal the Schwarzschild radius."

A SN makes a BH because an explosion compresses the core while the blast wave ejects the envelope. The core is pushed in by the failure of pressure support while the shock wave powered by nucleosynthesis in the outer regions ejects the envelope.

I'm still scratching my head, and removing splinters from under my nails...
So it's a BH if the mass fits inside its Schwarzschild radius? And the BH density can still be about the same as the density of air on earth (mass / volume inside Schwarzschild radius, supermassive BHs)?
One might think that in any given point inside such a BH, most of the mass is too far away to make gravitational field strong enough to stop light from escaping.
That is, if the mass becomes more or less equally spread within the Schwarzschild radius.

Also, if r(Schwarzschild) = 2GM/c^2 where r(Schwarzschild) implies a sphere, I guess it, kind of says, that the limiting density is M/r(Schwarzschild) = c^2/(2G)?

[turboscrew]

The "limiting density" should have been in quotes, because it's not density, but something just related to the density.

[notFritzArgelander]

I'm thinking that, neutron star keeps being a neutron star, because the gravitation of the "halves" make very high pressure in the middle. So much mass so near. I'd think if the density becomes low, the "edges" of the mass are far, and the gravitational pull of the other half becomes much smaller. Or why is it, that a star can become a black hole even if it looses mass (SNR)?

Understood. But here the informal model you've constructed is misleading you a bit about BHs although it works for neutron stars. I remember being surprised in the same way when I was doing homework problems in GR 50 years ago. One was, compute the Schwarzschild radius that corresponds to the density of water. NSs and BHs are very different and the model of "gravity holding it together" works for the NS but fails for the BH. A BH forms only when an event horizon forms and the criterion for that is "does the mass inside this radius equal the Schwarzschild radius."

A SN makes a BH because an explosion compresses the core while the blast wave ejects the envelope. The core is pushed in by the failure of pressure support while the shock wave powered by nucleosynthesis in the outer regions ejects the envelope.

I'm still scratching my head, and removing splinters from under my nails...
So it's a BH if the mass fits inside its Schwarzschild radius? And the BH density can still be about the same as the density of air on earth (mass / volume inside Schwarzschild radius, supermassive BHs)?
One might think that in any given point inside such a BH, most of the mass is too far away to make gravitational field strong enough to stop light from escaping.
That is, if the mass becomes more or less equally spread within the Schwarzschild radius.

This is one of those places where thinking about an event horizon in terms of "force of gravity" doesn't work. In GR, remember, gravity isn't a force, it is the curvature of spacetime itself.

In Newton, there is no spacetime curvature and at a deep level, this is because there is no speed limit for causation. Gravity acts at a distance. Gravitational forces are a simple linear function of the mass acting. Double the mass and double the force. The Newtonian version of a BH is a Dark Star: https://en.wikipedia.org/wiki/Dark_star ... mechanics)

The BHs of GR are much different from a Newtonian Dark Star and this is because 1) there is a speed limit for causation, 2) there is no action at a distance, 3) the effects of spacetime curvature are NONlinear. If you double the matter present, you MORE than double the spacetime curvature. In fact you can build a perfectly working BH with NO matter only the mass-energy of spacetime curvature all by itself. This sublink from the link above tells the tale. https://en.wikipedia.org/wiki/Dark_star ... lack_holes

The formation of an event horizon is something that does not happen with Newtonian Dark Stars. Radiation can rise from the surface but it falls back. GR BHs can emit Hawking radiation but that is because the curvature of spacetime is tidally effecting the vacuum near the event horizon. Nothing comes from the event horizon itself.

Yes, SMBHs can have less than the density of air and water. https://en.wikipedia.org/wiki/Schwarzsc ... black_hole

The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density.[13] In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at a given fixed density (in this example, 997 kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 10^8) M☉, its physical radius would be overtaken by its Schwarzschild radius, and thus it would form a supermassive black hole.

So I've given up on thinking of "gravitational force" when it comes to BHs. I think it misled me when I was a student and as soon as I calculated the water density BH I quit the notion.

[notFritzArgelander]

The "limiting density" should have been in quotes, because it's not density, but something just related to the density.

Yes.

[turboscrew]

The "limiting density" should have been in quotes, because it's not density, but something just related to the density.

Yes.

I think, that led me astray. I realized, when I played with numbers of M87*.
It's related to 3rd root of "volume"!

AU = 149 597 871 000 m = 1.5x10^11 m
Msun = 1,989x10^30 kg

Schwarzschild:
M/r = c^2/2G = 9x10^16 / 1,3348x10^-10 = 6,7x10^6 m^3kg^-1s^-2

M87*: density = ~ 1 kgm^-3
mass = (6.5 ± 0.2stat ± 0.7sys) × 109 Msun
Schwarzschild radius 5.9×10−4 parsecs (1.9×10−3 light-years) 120 AU)
r = 1.8x10^13 m
M = 2.18x10^32 kg
M/r = 1.21x10^19
r^3 = 5,832×10^39 ... didn't need to go forward from this...

[notFritzArgelander]

The "limiting density" should have been in quotes, because it's not density, but something just related to the density.

Yes.

I think, that led me astray. I realized, when I played with numbers of M87*.
It's related to 3rd root of "volume"!

AU = 149 597 871 000 m = 1.5x10^11 m
Msun = 1,989x10^30 kg

Schwarzschild:
M/r = c^2/2G = 9x10^16 / 1,3348x10^-10 = 6,7x10^6 m^3kg^-1s^-2

M87*: density = ~ 1 kgm^-3
mass = (6.5 ± 0.2stat ± 0.7sys) × 109 Msun
Schwarzschild radius 5.9×10−4 parsecs (1.9×10−3 light-years) 120 AU)
r = 1.8x10^13 m
M = 2.18x10^32 kg
M/r = 1.21x10^19
r^3 = 5,832×10^39 ... didn't need to go forward from this...

Yeah, it's tricky in GR because the spacetime curvature also contributes to the mass!

[turboscrew]

These things are dangerous. I was planning to pay some bills, do the dishes and watch some TV, but I kept thinking about this (and kind of still am), and it's almost 10 PM local time, and workday tomorrow...