Not necessarily. A black hole doesn't have any stronger gravity than an ordinary object of the same mass. And matter falling into the hole would radiate strongly (the paper calls this "accretion luminosity"), which would help to maintain an equilibrium with the rest of the star. That's the kind of model the paper is studying.
How long such an equilibrium can last is a different question. The paper only briefly comments on this when it says that the time scale of the numerical simulations they did is of the same order as the hydrodynamic timescale of the Sun. That means, roughly, the time it would take the Sun to collapse to a white dwarf if fusion reactions in its core stopped, which is, I believe, tens of millions of years. So a star with a black hole at the center would not have the same lifetime as an ordinary main sequence star with similar mass, but it would have a long enough lifetime that would could not conclusively rule out that at least some stars we see have black holes at their centers.
A black hole at the center of a gaseous body would mess with the fusion cycle would it not? There’s no pressurized core at the center. Just a drain that all pressure exits into.
> A black hole at the center of a gaseous body would mess with the fusion cycle would it not?
Not necessarily. That's the sort of question the paper investigates, and it finds models for which fusion can continue in the star's core for an extended period of time.
> There’s no pressurized core at the center.
Yes, there is, because, as I noted, the matter falling into the hole radiates strongly, and the radiation has pressure.
How do you capture a PBH unless there’s substantial, fast mass (momentum) transfer from the star to the black hole? Otherwise the ballistic trajectory would carry it out and through. Wouldn’t you be more likely to find a PBH orbiting a main sequence star? Or gone altogether?
It came to me while doing some housework that this feels like “what if the moon crashed into the earth?” The moon cannot crash into the earth. Any alien that could make that happen would be so terrifyingly powerful they wouldn’t have to crash the moon into the earth. It would be the twentieth most interesting way to doom us. Tidal waves would be easier.
While your statement about the ballistic trajectory is true in the short term, over longer time scales (my off the cuff guess is thousands of years, much shorter than the time scale covered by the numerical simulations in the paper), there will be momentum transfer due to the PBH perturbing the star's matter as it passes through, and the PBH will settle into the center of the star if there are no other perturbations (i.e., no other massive bodies near enough to affect the process). The paper doesn't discuss the capture process in any detail, but I suspect that something like that is what they have in mind.
Matter falling into a spinning black hole surrounded mostly by vacuum forms an accretion disc. But friction and heating and radiation will occur in infalling matter no matter how it is falling in. A black hole inside a star would probably not just have an accretion disc, it would have accretion happening in all directions. But the accretion would still involve friction and heating and radiation.
> the sun's schwarzchild radius is more like inches than Angstroms.
No, it's not inches, it's about 3 kilometers.
But the holes at the center of stars that the paper is talking about have tiny masses, much, much smaller than those of the stars they are inside. Their schwarzschild radius could indeed be of the order of Angstroms.
it would only be a pinhole at first, though start to grow quite rapidly(? no idea in what time scale?) and at some point consume the sun quite violently from within, no?
The numerical simulations in the paper go on for a time on the order of the Sun's hydrodynamic time scale, which is tens of millions of years. After that time has elapsed, yes, the star could be completely consumed by the hole.
"For many readers, intuition from astrophysics
will suggest that a star that captures a PBH will
be short lived and look nothing like a star dur-
ing that life. However, we will show that stars
with very low mass PBHs could be very long lived
with many surviving their entire main sequence
phase. Ultimately the evolution is highly sensitive
to the accretion physics, which is the subject of
the following sections."
I hadn't known this until recently, but it's theorized that in the early universe there were super huge stars that had black holes in them - https://en.wikipedia.org/wiki/Quasi-star
It sounds like you’re conflating time dilation with the concept of light being unable to escape once it crosses an event horizon.
Nothing is actually “frozen” around a black hole, but if you accept that light cannot escape once it passes an event horizon then it follows that there must have been one final moment when light still could escape. The light that was able to escape in that final moment would reach your eyes as a “frozen” image of the object where it previously was the exact moment before gravity became too much to overcome.
What's mind bending to me is that a second object just short of that point _also_ sees the first object frozen. It doesn't matter how close you get to the horizon, the image of an object that got there first is still infinitely far in your future.
Yeah, that really is so neat to visualize. That there’s a hard line when the escape velocity reaches exactly the speed of light, and poof. Frozen image of the past right in front of your eyes.
And think… once we crossed the event horizon as observers ourselves (leaving a frozen image for observers behind to see), wouldn’t we see the “tracers” of images the person before us left behind every moment we move closer to the singularity? Edit: no… we never would see any light (in front of us) again by definition when crossing the horizon, duh lol.
When referring to black holes, "falling in" means going past the event horizon. For all practical purposes for us on the outside of the singularity, this is "having fallen into the black hole" as any object is gone to us forever once having done so. We don't use falling in to mean touching the singularity, which as you noted, does indeed take infinite time. Using the definition this way isn't particularly useful.
This is my understanding: It takes an infinite time to cross the event horizon from the perspective of a distant, stationary observer, but a finite time from the perspective of the object that is actually falling towards the black hole. Once past the event horizon, reaching the singularity takes a finite amount of time from the perspective of the falling object. From the point of view of a distant external observer, time from event horizon to singularity is a meaningless question because the events inside the event horizon are causaully disconnected from the events outside of the event horizon.
Your explanation is wrong. For an outside observer, time dilation approaches infinity at the event horizon. Singularities don't even exist for an outside observer, they have yet to happen in the infinite future.
Is that kind of the same as the idea that if you are approaching a wall but each step is only 50% of the rest of the way to the wall, so you would never reach the wall no matter how close you got?
When thinking of dark matter, I've always wondered how we actually measure the density of black holes. My confusion lies in how we can derive the mass at the hyper-quantum state at the center of a black hole from the gravitational waves we observe as it loses energy.
I'm not a physicist so my question might be silly.
> I've always wondered how we actually measure the density of black holes.
We don't. The density of a black hole is not even a well-defined concept; black holes are not like ordinary objects.
> My confusion lies in how we can derive the mass at the hyper-quantum state at the center of a black hole
There is no such thing. A black hole is vacuum inside. The "mass" of the hole is not due to "stuff" sitting inside it; it's a global property of the hole's spacetime geometry, that maintains itself because of the nonlinearity of the Einstein Field Equation.
> from the gravitational waves we observe as it loses energy.
An ordinary black hole in our universe will be gaining energy, not losing it--if for no other reason that CMB radiation is shining on it. But the black holes we see all have matter falling into them as well.
As for detecting gravitational waves, except for violent events like black hole mergers, we don't detect any; what few such gravitational waves there are are far too weak for us to detect.
To what degree would a non-spinning, non-moving black hole necessarily produce even very weak gravitational waves? Would some be produced as matter/energy reaches it? If so, would no gravitational waves at all be produced if nothing was reaching it, hypothetically? (I suppose these same questions apply to all massive objects.)
> To what degree would a non-spinning, non-moving black hole necessarily produce even very weak gravitational waves?
If it's perfectly non-spinning, and nothing is falling into it, then it emits no gravitational waves at all.
If matter or energy falls in, and does so in a manner that is not spherically symmetric (which will most likely be the case), then some very weak gravitational waves will be emitted. But they will be much, much too weak for us to have any hope of detecting them. Even a gravitational wave detector like LIGO in the same stellar system would have difficulty detecting them.
> As for detecting gravitational waves, except for violent events like black hole mergers, we don't detect any; what few such gravitational waves there are are far too weak for us to detect.
I thought LIGO and VIRGO had been detecting gravitational waves for the last 4 years pretty regularly (i.e. once a week).
Yes, but not because of "stuff" inside it. As I said, the mass is a global property of the spacetime geometry.
> and a volume defined by its event horizon.
No, it has a surface area defined by its event horizon. But you can't compute a meaningful volume from this surface area. You can, of course, plug the surface area into the formulas of Euclidean geometry, but the number you get will have no physical meaning for a black hole. A black hole has no well-defined volume at all--indeed, one can find spacelike surfaces inside that are infinite in extent, even though it has a finite surface area.
I don’t know if I really agree that a black hole’s mass is not because it has “stuff” (that is, massive entities) inside it. How do you argue that?
In simpler terms, let’s say a star has a mass just below the limit of making it a black hole. Then, a planet collides and it crosses the threshold. Are you saying the “stuff” disappears ?
Because the solutions of the Einstein Field Equation that describe black holes are vacuum solutions. "Vacuum" means "no matter or energy".
> let’s say a star has a mass just below the limit of making it a black hole.
There is no lower limit to the mass of a black hole.
There are maximum mass limits for white dwarfs and neutron stars, and stars more massive than those limits (after they have undergone supernova explosions and probably shed a large portion of their original mass) will collapse to black holes.
As for what happens to the matter in the original object that collapses to a black hole, it reaches the singularity at the center of the hole and is destroyed. But anyone falling into the hole after the collapse will never encounter that collapsing matter; all they will see is vacuum.
We don’t actually know what happens to the matter when it reaches the singularity. Having a singularity effectively means “we don’t know what happens there”.
More precisely, physicists believe that the presence of the singularity in this solution of the Einstein Field Equation means that GR breaks down there and we will need some other theory (the best candidate at this point appears to be a quantum gravity theory) to figure out what happens there. But unless and until we discover that other theory, GR is the best we have and the best we can do is to describe what it predicts and acknowledge the limitations.
> I’d argue that GR literally provides no prediction for what happens at the singularity
That's false; GR does make a definite prediction: that curvature invariants increase without bound as the singularity is approached, but that they are finite everywhere in the actual spacetime (see further comments below). (Actually it's more nuanced than that; there are cases where there are incomplete geodesics, which is how "singularity" is actually defined in GR, but not unbounded invariants. But those are edge cases that aren't relevant to what we're discussing here.)
The Stack Exchange thread's claim about geodesic incompleteness is misleading. The actual singularity--heuristically, the "point where things become infinite"--is not included in the spacetime manifold. It is an abstract "boundary point" that is not part of spacetime. What is actually included in the manifold is perfectly well-defined, with nothing infinite anywhere, and is a perfectly self-consistent mathematical model that makes perfectly valid predictions for everything in it.
The Stack Exchange commenter basically doesn't like the fact that GR says "sorry, your model ends here, you can't extend it any further", which is fine, but it's not the same as saying GR must be wrong when it says that. It's just something many physicists are uncomfortable with and so they are looking for a model that doesn't have that property, like quantum gravity. But that's no guarantee that they will find one, nor is it a guarantee that GR must end up being overridden in this regime. It's just a best guess of many physicists at our current state of knowledge. Nor does it mean that GR doesn't make definite predictions; it just means GR's predictions are ones that most physicists would not like having to be stuck with if that's how it turns out. But nature doesn't care what humans like or don't like.
> gravity propagates at the speed of light... And light is not fast enough to escape the black hole.
Gravity doesn't have to get out of the hole. The gravity you feel outside a black hole is due to the global spacetime geometry, not to any "force" coming out of the hole. If you want to attribute it ultimately to the presence of matter, it is the matter in your past light cone, which originally collapsed to form the hole, before it fell below the event horizon.
> Light is “fast enough” it just redshifts to nothing. Gravity has no equivalent
This is wrong in two ways. First, light at the hole's horizon does not "redshift to nothing"; it just stays at the same radial coordinate because of the curvature of spacetime. The "redshift to nothing" view is an illusion, created by a bad choice of coordinates; that illusion was corrected in the late 1950s and early 1960s by the discovery of better coordinates.
Second, gravity does have an equivalent to light: gravitational radiation. Gravitational waves travel on null geodesics, just like light, and any gravitational waves at the hole's horizon would stay at the same radial coordinate just as light does.
Let’s say there is a light bulb inside the event horizon. It emits a photon. From the light bulb’s perspective, it sees the photon speeding away at the speed of light.
From an outside observer, we never see the photon. It can’t make it out. But — the photon does exist, and it is traveling at the speed of light over a finite (though deeply warped in spacetime) distance. How does the photon not reach us then? Is it not going at the speed of light?
The redshift model applies here; the photon is redshifted until it has no energy from our frame.
To get density you need to know the volume in addition to the mass. As far as I understand, the volume is hard to measure and mostly theoretically derived, amd lensing and orbiting bodies would behave the same regardless of whether it was a point mass or low density sphere.
> the volume is hard to measure and mostly theoretically derived
Not even that. The "volume" of a black hole is not even well-defined. A black hole doesn't work like an ordinary object.
> lensing and orbiting bodies would behave the same regardless of whether it was a point mass or low density sphere.
First, a black hole is definitely not a "point mass". Second, the density of a black hole is also not well-defined.
Lensing and orbiting bodies do exhibit unique properties close enough to the black hole's horizon, but unfortunately we would have to be relatively close to the hole (meaning, in the same stellar system, not light years away) to distinguish them.
> A black hole doesn't work like an ordinary object.
Black holes are ordinary objects, if they are anything at all. Take any normal object and give it the mass of a black hole, and what do you have?
To claim that a black hole “doesn’t work like normal matter” seems to ignore that these entities have come to exist “normally”, or rather, through a natural course of events.
It’s not that the black hole “doesn’t work like normal matter”, but rather that you refuse to accept that normal matter with the mass of a black hole (and hence, the observable properties we associate with black holes) are still “normal objects”.
When objects of a certain class display certain properties, it’s not accurate to say “that’s not normal.” Instead, it would be accurate to say, “that is the normal behavior of objects once they reach this class or state.”
> Black holes are ordinary objects, if they are anything at all.
No, they aren't. Their spacetime geometries are very, very different from those of ordinary objects.
> Take any normal object and give it the mass of a black hole
There is no such thing as "the mass of a black hole". What distinguishes a black hole from other objects is not its mass, but its spacetime geometry. That's particularly true for the holes studied by this paper, which are far smaller than the ones we actually see with our astronomical observations.
The rest of your post is simply wrong. A black hole is not made of normal matter; it's vacuum. I'm sorry, but you simply don't understand the physics of black holes. A good free online reference is Sean Carroll's lecture notes on GR:
> What distinguishes a black hole from other objects is not its mass, but its spacetime geometry
Fair enough. Primordial black holes are a good theoretical example of environmental density conditions being perhaps a larger factor than mass even. My point was that it was still matter. It doesn’t matter if you squish it all down - it’s still matter.
> A black hole is not made of normal matter; it's vacuum.
When we talk about black holes, some might be referring to the event horizon, and others the singularity which makes the event horizon possible. But I’m not sure what you mean when you say that a black hole is made of vacuum. Are you saying that the singularity of a black hole is a vacuum? And not matter?
I don’t think black holes have a well defined “density” in that sense? I think we just use the event horizon as the “size” (which therefore has a simple relation to the mass.)
Longer answer: Let's assume you have a "star" (more later) and teleport it into the middle of a Jupiter-like object or other such planet. Jupiter isn't a stars and generally once you get to about thirteen Jupiter masses, fusion begins (for a gas giant) and now it is a star. So, let's go over our stars:
1) Red dwarf: This is the largest "star" object that might fit inside of Jupiter. Some are only 70,000 kilometers in diameter and so could fit inside of Jupiter. Upon teleportation, equilibrium is disturbed and the surface of the red dwarf, pulling upon the gases at hundreds of gs, simply absorbs the gas giant with some alacrity. Likely some stellar brightening, changes in color, for a while.
2) White dwarf: Smaller than a red dwarf, their diameters are only a few thousand kilometers, give or take. You get the same results as a red dwarf but, if the gas giant absorbed has enough matter or the white dwarf is already on the edge, you might get a nova. Not a supernova, that's a different system and a different process. Just a nova.
3) Neutron star: Much smaller than your white dwarf and it will have a larger mass. Again you get a collapse of the gas giant but likely no nova since the gas hits the surface and its electron degeneracy pressure is overcome, blah blah, and everything turns into just another layer of neutrons.
4) Black hole: Not really a star any longer, but some older classifications included it and I will add it for completeness' sake. Much like #3, but instead of neutrons the black hole simply increases in size. You may or may not get an accretion disc, depending on the rotations of your gas giant and your black hole.
So, in all four cases, none of the stars could exist within the gas giant where the gas giant would remain stable.
It does not make really sense to talk about 'binary star'. It should be a 'binary stellar system' with 2 stars involved. With this meaning, if you intend to say Jupiter is a failed star and if it had been a star we will be living in a binary stellar system (Jupiter as a star + the Sun), then yes.
Two sources of sunlight, often on opposite sides of the Earth, certainly would have changed the path of evolution, possibly even back as far as primordial slime.
What if looking backwards in the solarsystem is looking at the same planet, just in the past? Mercury, venus, earth, mars, saturn, uranus, neptune... all the same planet.
Neptune, gasses condense as they get compressed by gravity
Uranus, a small core surrounded by compressing gas
Saturn, we can see the accretion disk formed before it gets compressed to more mass (heard we just found hydrogen cyonide here as well!)
Mars, a dense planet with no atmosphere. Water under the crust, though!
Earth, hydrogen chloride + h2o = BAM! Life
Venus, too close to the sun to sustain life
Mercury, a hot planetary body which is smaller due to it's matter being absorbed by the Sun
"Once in its post-main sequence phase the Hawking star becomes fully convective and slowly swells over multiple Gyr to about 10 R⊙ and about 10 L⊙ causing them to appear as a sub-subgiant star, joining a relatively sparse population on the HR diagram."
and then
"The resulting increase in accretion luminosity causes the inner convective region to grow outwards, mix the He core with the H-burning shell, and quench fusion."
Would the aftermath of all this be observable? Once fusion is quenched wouldn't the gas cool rapidly?
Why did you left out the second part? "... Despite this detail, our goal in this work to convince the reader that this question is interesting and that work studying stars with central black holes is well motivated. If primordial black holes exist then they may exist in sufficiently large numbers to explain the dark matter in the universe..."
But in the scenario in this paper… if there were a black hole in the sun does that make the plasma on the outside a natural Dyson sphere capturing energy from a black hole? Or maybe not natural tinfoil hat.
https://en.wikipedia.org/wiki/Thorne%E2%80%93%C5%BBytkow_obj...