I think they're pointing out that while the speed of the earth relative to the sun is 30 km/s, its speed relative to the center of the galaxy is quite a bit faster, which may be a fairer comparison to what's being discussed in the original article.
They're not even remotely comparable. Tangential speed x where r=several thousand light years results in SUBSTANTIALLY less centripetal acceleration than the same tangential speed where r=a few AU.
I wonder if you could model this in Universe Sandbox [0]? (I live in Seattle so I've met the author Dan Dixon a few times at meetups but have no other relationship to it)
Despite the other replies, at only 1% of the speed of light you could set up a reasonably similar situation. The deviations between Newton and Einstein here would be significant if you were trying to literally plot an orbit for your visiting spaceship (and why the bloody hell would you want to do that?!), but not if you just want to watch two high mass objects dance around each other really quickly for a bit.
My question would be more about whether the simulation has sufficient granularity to avoid the star flying away due to the time step being too large, rather than concerns about relativity. And of course Universe Sandbox won't be simulating the black hole tearing away bits of the star, or at least, so I'd presume.
If I recall my physics correctly the most important thing it would miss is the orbital energy of the start slowly being radiated away as gravity waves and the star eventually being swallowed by the black hole.
The two objects are the size of our sun, the green one represents the black hole.
I put in the orbital distance as 2.5 times the Earth to Moon distance as stated in the article, and just tweaked the mass of the black hole (green orb) until the star orbits once every 30 minutes. The mass of the star will hardly matter. The mass of the black hole in this model is 60 solar masses.
The model timestep is here is 1 minute, five or ten minutes should still work for this engines integration scheme. Its a Newtonian model, at 0.01 lightspeed there will be innaccuracy but I guess just a few percent in measurements.
Does it account for relativity?
No, the physics in Universe Sandbox ² is currently only
Newtonian.
Why?
The short answer is that you need a supercomputer to
accurately simulate general relativity.
Jenn, astrophysicist and Universe Sandbox ² developer,
explains more in a blog post: "General relativity
requires simulating the spacetime itself. That is,
taking your simulation space, discretizing it to a
hi-res 3-D grid and checking the effect that each and
every point in that grid has on all neighboring points
at every timestep. Instead of simulating N number of
bodies, you are simulating a huge number of points.
You start with some initial data of the shape of your
spacetime and then see how it evolves according to the
Einstein equations, which are 10 highly non-linear
partial differential equations."
We are, however, interested in adding in a few features
which would address some effects of relativity. One
example is setting gravity to travel at the speed of
light, instead of instantaneously taking effect as it
currently does. You can read more about these in
Jenn's blog post: Gravitational Waves & Universe
Sandbox ².
First and second order corrections are a lot more reasonable to calculate than the whole theory!
Furthermore calculating the whole theory runs into interesting challenges where the coordinate system is twisted and and distorted but underlying space-time is not. For a well-known example, a black hole can be described with both Schwarzschild coordinates and Kruskal–Szekeres coordinates. The first coordinate system blows up at the event horizon, the second doesn't. The fact that it blows up is due to a bad choice of coordinate system there, and not due to local space time being particularly bizarre at that spot.
How cool - asking the question "does gravity propagate at the speed of light and if so what impact does that have on orbital dynamics" was the event that led me down the path to my PhD, so it's awesome the answer to the question is now (or soon to be?) baked into a science toy.
How much temporal dilation would a relativistic orbit about a frame-dragging massive object create? Would the black hole or other objects orbiting it look weird (relatively--hehe--speaking).
It's not really until you get up near 90% of the speed of light, where dilation starts getting insane. That's when the curve starts to sharply jump straight up.
As a rule of thumb, relativistic effects are very small below 5-10% of the speed of light. You may still need to calculate them if you want very high precision, like for GPS.
If anyone is curious, the reason is that many/most special relativistic effects are proportional to gamma = 1/sqrt(1-v^2/c^2), with gamma = 1 being non-relativistic. Even at v=20% of c, gamma is only 1.02 (a mere 2% effect).
General relativity also accounts for gravitational/accelerational effects, in addition to the speed-related effects. For example, in the Schwarzschild metric[1], effects such as time dilation are on the order of 1-phi/c^2 where phi=GM/r. Or expressed in terms of "g-force": phi=gr.
Yes, but doesn't that ignore the gravitational acceleration? Time dilation isn't just speed, it's also acceleration. Even if you could hover very near the event horizon the time dilation would be severe.
Yes, but doesn't that ignore the gravitational
acceleration
Gravitational acceleration doesn't exist (in GR). All bodies are stationary in GR and observe other things moving in reference to themselves.
What we perceive as gravitational acceleration is just objects traveling in straight lines (at constant speeds) though 4D space-time. Circular orbits are just straight lines of constant velocity bent around by the local curvature of space-time (which can be caused by a local density of mass-energy).
The idea of acceleration assumes a force is acting on a body. Gravity isn't a force in General Relativity. It is the shape of the universe.
> Gravitational acceleration doesn't exist (in GR).
A better way of stating this would be that objects moving solely under gravity have zero acceleration in GR, because in GR, acceleration means proper acceleration--what is measured by an accelerometer. Objects moving solely under gravity are in free fall.
> All bodies are stationary in GR and observe other things moving in reference to themselves.
This isn't correct. There is no requirement that an observer in GR must use coordinates in which they are at rest.
> Time dilation isn't just speed, it's also acceleration.
That's not correct. Gravitational time dilation isn't a function of acceleration, it's a function of gravitational potential, i.e., how deep you are in the potential well of the source.
(Also, an object that is in a free-fall orbit has zero acceleration in GR, since in GR acceleration is proper acceleration--what is measured by an accelerometer.)
Seeing as the star is in close proximity to a blackhole it would likely be similar to the Kerr-Metric [1] (as we _should_ assume the black hole as some spin).
The white star has non-trivial mass of its own which greatly complicates the curvature of the local space-time region and render the Kerr-Metric equations lacking.
Unless the hole is rotating extremely rapidly (which I don't see mentioned), the difference between the Kerr metric and the Schwarzschild metric (which is what I used for the formula I posted upthread) is too small to matter unless you are really close to the hole's horizon.
You got me curious, and I wanted to put numbers around this. It's worth noting that the actual paper claims only this is a black hole candidate, and is not certain it's a black hole (despite the Science alert headline).
The paper guesses that the black hole is ~ 1 solar mass, so the Schwarzschild radius would be about 3 km.
The distance is about 2.5x the earth-moon, which is about 10^6 km.
If I read this right, that 1% number is a guess. That is, they know it orbits in 28 minutes. They don't know the radius of the orbit. They guessed what the mass of the black hole is, and from that solved for the radius of the orbit, and therefore found the velocity - but it's all based on the guess of the black hole mass.
Once I read on a book, that there may be a star so huge that it orbits a black hole at half of the speed of light, i.e., 150,000 km/s. Is this possible?
No. That size, that speed, would see the star ripped appart by tidal forces. The situation would not last long. The star wouldnt be a star, more a bunch of gas being accelerated/heated into a stream of particles mostly flung away into space.
I think that star size is irrelevant here - any massive object will need to have the same speed to hold a given orbit. It's black hole mass and star's proximity to black hole that are in this equation.
Assuming star is much lighter than the black hole, or course.
But it's possible to have a star that is heavier than a black hole.
Say you had a binary star system of two supermassive stars. The smaller one goes nova because it runs out of fuel first. The core starts to collapse, meanwhile the twin is scooping up the ejecta, and the star and the black hole start getting closer together...
>Things become black holes by being dense, not by having large mass.
not really. The larger the mass the less dense it has to be when it fits into its Schwarzschild radius. For example, our visible Universe - 46B ly radius - has Schwarzschild radius of 13.7B ly (that number sounds strangely familiar, isn't it? and may give rise to various speculations :), ie. it would have to be just 64 times denser that it is now, ie. like 64 atoms/m3 instead of the current 1 atom/m3.
"The Schwarzschild radius of an object is proportional to the mass. "
Thus we can see that given the same density mass grows as a cube of the radius of containing sphere, and thus Schwarzschild radius of such a mass would grow as a cube of that sphere radius too. So if a mass grows it is possible for it to lose density pretty fast, like the sphere's radius square fast, and still fit into its Schwarzschild radius.
Yes, absolutely - black holes don’t need singularities inside them in order to be black holes. Just enough mass in a small enough volume.
(Of course, we don’t actually know whether stellar or galactic centre black holes have singularities inside them - we just don’t know of any process that will prevent one from forming in current physics.)
> black holes don’t need singularities inside them in order to be black holes.
They do according to the standard GR model. Speculations about holes not having singularities inside them are quantum gravity speculations and we have no way of testing them experimentally any time soon.
No, just inflation taking the rest of the universe over the horizon - I believe it’s the dynamic effects of being in an inflationary universe that mean that the standard GR results for black holes don’t apply, at least according to the references I read. (I can’t pretend to be able to derive this stuff personally.)
> so there's a possible that the visible universe is a black hole?
No. The universe is expanding. If it were a black hole, it would not be expanding. The calculation of how much mass has to be inside what radius in order to form a black hole assumes that the matter is static (or collapsing); if it's expanding, the calculation is meaningless.
I'm not sure because the above result doesn't say anything about the distribution of such mass, and intuitively since the light cone tips over once you're past the event horizon, everything inside is converging towards the singularity following a law that may prevent any black hole inside black hole from existing (but that's way over my head now).
>everything inside is converging towards the singularity
singularities are result of the pure abstract model of [mathematically] continuous spacetime. In real live at small scales the continuity gets broken and as one of the results of it we have QM - if you think about a typical large, star sized, black hole than you can see how degenerate matter in the center would provide the opposite pressure against collapse into singularity similarly like it happens in neutron star. The difference here is that in neutron star the limited existing mass of the star limits the resulting neutron degeneracy level achieved. In case of a black hole the process doesn't stop and as more and more mass comes in the degeneracy goes further/higher with the neutrons being pushed into even higher energy levels and starting to be teared apart into separate quarks and gluons, and as even more mass/energy comes in the quarks get teared apart even further one from another with the new pairs of quarks appearing as a result... That would provide the pressure opposing collapse into singularity. The more incoming gravitational mass/energy pressure the stronger the response. Btw, that boiling quark-gluon soup looks suspiciously like something that is hypothesized as what was in the beginning of our Universe ( what could have triggered the Big Bang explosion/expansion? - may be merge with another super-hyper-gigantic black hole).
> if you think about a typical large, star sized, black hole than you can see how degenerate matter in the center
There is no degenerate matter in the center of a black hole; it's vacuum inside. A black hole is not an ordinary static object with "stuff" inside, that happens to have a radius smaller than the Schwarzschild radius for its mass. It's a fundamentally different kind of thing: it's made of spacetime curvature, and that's all.
> In case of a black hole the process doesn't stop and as more and more mass comes in the degeneracy goes further/higher with the neutrons being pushed into even higher energy levels and starting to be teared apart into separate quarks and gluons, and as even more mass/energy comes in the quarks get teared apart even further one from another with the new pairs of quarks appearing as a result... That would provide the pressure opposing collapse into singularity.
There have been speculative models along these lines, but none of them have any experimental support.
> that boiling quark-gluon soup looks suspiciously like something that is hypothesized as what was in the beginning of our Universe
Same comment--there are speculative models along these lines, but none of them have any experimental support. Figuring out a way to test these models, as well as many other different speculative models of the very early universe, is an open area of research in cosmology.
> In real live at small scales the continuity gets broken
This is a common speculation in quantum gravity, but at this point that's all it is: a speculation. We have no evidence that spacetime is not continuous. And given the predicted scale at which continuity would break down if the quantum gravity speculations are correct (about twenty orders of magnitude smaller than the smallest scale we can currently probe), we aren't likely to be able to test those speculations any time soon.
> It would be totally plausible to have supermassive black holes inside of universe-sized black holes
No, it wouldn't. You can't have one black hole inside another one. A black hole is a region from which light can't escape to infinity. There can't be such a region inside another one; that makes no sense.
If you define a black hole as a clump of matter entirely contained within its own Schwarzschild radius, then it seems that yes, you can have one inside of another.
Even if you define a black hole as "a region from which light can't escape to infinity", a theoretical black hole inside of another black hole doesn't violate this definition.
No, I'm using the term "black hole" as it is actually defined in physics.
> If you define a black hole as a clump of matter entirely contained within its own Schwarzschild radius
Then you are not defining the term "black hole" as it is actually defined in physics.
> Even if you define a black hole as "a region from which light can't escape to infinity", a theoretical black hole inside of another black hole doesn't violate this definition.
Yes, it does, because once you are inside the boundary of one such region, that's it. There can't be a second boundary further inside; if there were, there would have to be a region from which light can escape to infinity (outside the second boundary), inside a region from which light can't escape to infinity (inside the first boundary). That's not possible.
In other words, if one black hole falls into another, what you get is not two black holes, one inside the other. What you get is one black hole. The two holes merge into a single hole.
> > If you define a black hole as a clump of matter entirely contained within its own Schwarzschild radius
> Then you are not defining the term "black hole" as it is actually defined in physics.
Again, you're playing semantics here for literally no point other than to be a pedant on the Internet. JUST AS COOL AND INTERESTING is a clump of matter that fits inside its own Schwarzschild radius, that's inside a universe-sized black hole. In other words, the exact kind of structure I was talking about before you decided to derail the conversation.
What the hell happened to you that you feel the need to remove people's wonder and enjoyment of science by pedantically correcting non-precise word choice?
> Yes, it does, because once you are inside the boundary of one such region, that's it.
Being inside the boundary of such a region does not preclude a subregion from itself having an escape velocity greater than the speed of light. Such an object seems to me that it still has all of the interesting properties of a black hole, while existing inside of a black hole.
Again, do you feel like being a pedant contributed positively to this conversation in any way?
> you're playing semantics here for literally no point other than to be a pedant on the Internet
Physics insists on precise terminology for a reason. It's not just pedantry.
> JUST AS COOL AND INTERESTING is a clump of matter that fits inside its own Schwarzschild radius, that's inside a universe-sized black hole
The only difference is that the clump of matter contains matter, while the universe-sized black hole can be idealized as vacuum (or at least as being so much lower in density than the clump of matter that this density can be ignored when you're analyzing the clump of matter). But that has nothing to do with any properties related to black holes. See below.
> Such an object seems to me that it still has all of the interesting properties of a black hole, while existing inside of a black hole.
And my point is that this is not correct, as a matter of physics, not words. There are no "interesting properties of a black hole" which change in any way when you cross the boundary from the universe-sized vacuum region to the clump of matter region. The only property that changes is the density of stress-energy. As far as any "interesting properties of a black hole" are concerned, there is just one region.
Here's another way to put it: when you think of the clump of matter inside the universe-sized black hole as "fitting inside its own Schwarzschild radius", you are calculating the Schwarzschild radius based on the mass of the clump of matter. But that calculation only has physical meaning if the clump of matter is isolated--i.e., if it is not inside the universe-sized black hole. If the clump of matter is inside the universe-sized black hole, then the only Schwarzschild radius that has physical meaning is the one you get by plugging in the total mass of the universe plus the clump of matter. (And even that is only meaningful if the "universe" in question is not expanding, as I've posted elsewhere in this thread.) So if you are thinking of the clump of matter as being a black hole because it fits inside its own Schwarzschild radius, you are thinking of it wrong, as a matter of physics. That's why the term "black hole" is not appropriate to describe it. It's not just a matter of words.
Actually I think I just gave the Big Crunch hypothesis. The universe can be expanding so long as it eventually collapses. Even in a normal black hole forming out of a star, some particles will happen to be heading out as the star collapses and then be dragged back in after the black hole forms.
> Actually I think I just gave the Big Crunch hypothesis. The universe can be expanding so long as it eventually collapses.
Even in this case it's not correct to say that the universe is a black hole. The spacetime geometry is very different. A black hole, as I've posted elsewhere in this thread, is a region from which light can't escape to infinity. But in a universe that will end up in a Big Crunch, there is no infinity: space has a finite volume (which increases up to maximum expansion and then decreases back to zero).
So admitedly, a few (bilion) years back, when the universe had a radius smaller than ~14B ly, it was sufficiently dense to be a black hole?
I mean, what ? Our universe did not lose mass in between (if we admit that it is a "closed" system), so at some point in the past, it grew out of being a black hole when it expanded above its Schwartzschild radius?
As long as you have ~uniform density out to the edge of the observable universe you get zero net gravity. Move over 1 light year and that particle also sees ~uniform density out to the edge of it's observable universe and you don't get a vast black hole.
> a few (bilion) years back, when the universe had a radius smaller than ~14B ly, it was sufficiently dense to be a black hole?
> at some point in the past, it grew out of being a black hole when it expanded above its Schwartzschild radius?
No and no. The calculations of the "Schwarzschild radius" corresponding to a given mass assume that the mass is static. They do not apply to an expanding universe.
> What would happen if the Moon were replaced with an equivalently-massed black hole? If it's possible, what would a lunar ("holar"?) eclipse look like?
The Schwarzschild radius of the Earth is something like 8mm. If the "moon" were to be visible to the naked eye, it would be more accurate to say that the planet orbits its moon.
Things can be turned into singularities a la the LHC, or they can be primordial black holes born via the big bang, but the only things that can "become" black holes are stars. Everything else must be turned into one by an outside force.
Wait. What? A star more massive than a black hole?
I must be missing something here. Once something reaches the mass of a black hole, it becomes a black hole. No? How is it possible for a mass to be greater than a black hole but not a black hole? Mass over distance?
no, there isn't some set mass that will make a black hole. A black hole is gravity overcoming the other fundamental forces. When a star dies and forms a black hole the force pushing outward from the fusion is overcome by the gravity of the star, but there isn't some threshold of size where this happens.
While true, this answer is a bit misleading. There is a minimum threshold for stellar black holes–the ones created through stellar evolution–it's called the Tolman–Oppenheimer–Volkoff limit.
> There is a minimum threshold for stellar black holes–the ones created through stellar evolution–it's called the Tolman–Oppenheimer–Volkoff limit.
That limit gives the maximum size of a neutron star, but it does not say an object smaller than that cannot form a black hole. In fact, it is considered likely that supernova explosions could cause an implosion that could form a black hole smaller than the limit, simply because it happens too fast for neutron degeneracy pressure to stop it before the implosion reaches the Schwarzschild radius.
I don't know absolutely nothing about black holes, but I think that amount of mass has nothing to do with it. It is the density what matters. Wasn't the LHC trolled about the possibility of creating tiny black holes?
No, stellar black holes have less mass than the stars they came from. When a star goes supernova it ejects much of its mass, the core can collapses into a black hole. Black holes don't form due to mass alone, but density of mass. Collapse the earth to the size of a golf ball and it'll become a black hole, but of course the earth doesn't have the necessary gravity to do that. Neither do stars, until their cores collapse and get dense enough to cross that line and become black holes.
What you're missing is that there's energy potential in nuclear structures, which can be released through nuclear fusion (and in some cases: fission, though that's not materially significant for stars).
What a star is, basically, is gravity and the strong nuclear force duking it out. Eventually, in most cases, the strong nuclear force wins. How long that takes, and where that ends up, depends almost entirely on the initial mass of the star itself.
For low-mass stars ("brown dwarfs"), there's only just barely enough gravitational pressure to stimulate nuclear fusion. The stars may radiate only in the infra-red, and have lifespans of trillions of years, after which they gradually cool to the background temperature of space, having exhausted their hydrogen. These are from a few times the mass of Jupiter to significantly less than the mass of our Sun.
A star such as our Sun has a lifespan of around 10 billion years. Gravity compresses its hydrogen and helium sufficiently that the atoms are no longer distinct, but form a plasma. In that, hydrogen atoms fuse (through several different chains, it can be complicated), producing first helium, then, as lighter elments (or at least their nuclei) are consumed, temperatures rise, and those in turn fuse, through carbon, nitrogen, oxygen, silicon, and finally resulting in iron, with core temperatures increasing all the while.
Iron is at the bottom of the nuclear potential curve -- you cannot release energy by fusing it (as you can lighter nuclei) or fissioning it (as you can heavier nuclei). Which means that gravity at this point wins, and the collapse of the star progresses to its next stage(s).
Incidentally, the rate of energy release by unit mass of the Sun is about 1/5 that of your own body. It's not that the Sun is highly energetic, but that there's so much of it.
Larger stars are fighting a stronger pull of gravity, so must release more energy with time to overcome its pull. They burn faster, and hotter. Basically: the bigger the star, the shorter its life, with some of the largest having a lifespan of only a few tens of millions of years.
There's a maximum star size (through normal formation) given that once a star begins hydrogen fusion the generated pressure drives off any additional potentially in-falling gas. This is roughly 40x a solar mass as I recall.
There may be models in which more massive stars can form through collisions, though I've no specific information on this.
In all of this: the star that forms may have enough mass to form a black hole, but so long as it can undergo fusion it will be able to resist that.
The ability to resist stops when silicon fuses to iron in the star's core. Once the silicon is exhuasted, a life-stage which takes about one Earth day, the core collapses. Depending on total mass, this may result in a white dwarf, a neutron star, or a black hole. It also generates absolutely immense heat (through pressure and kinetic energy) which rips through the rest of the star -- a nova or supernova. Much of the star's mass may be lost, and additional heavy elements (beyond iron) are formed. Which is to say: all of you that isn't hydrogen or helium, was once part of stellar fusion or a supernova (some heavy elements -- gold and platinum-series elements, may come from neutron-star collisions).
Which is how you can have stars more massive than black holes. For a while.
Keep in mind that surface temps could be anywhere from, say, a few low-thousands of K (dull red) to hundreds, possibly even tens. Constitution would likely be roughly 75% hydrogen / 25% helium, and up, with some lithium and possibly higher metalicity constituents.
What you wouldn't have though is a high-silicate crust with a bunch of CNO -- carbon, nitrogen, and oxygen.
Temperature and chemistry can both be ascertained through spectral emissions (wavelength corresponds to temp via blackbody, emission or absorption spectra to chemistry).
I'm not an astronomer though I've got a pretty good lay grasp of the subject. There may well be some literature on dwarf star chemistry and temperature, and Wikpedia is likely a good starting point.
I am not an astronomer, but IIRC, stars go through their fuel the faster the more massive they are. So in a binary system, ignoring mass transfer between the two, the more massive partner goes supernova first (assuming it's massive enough).
(One could, however, conceive a scenario where a black hole and a star more massive than the black hole happen to run into each other in such a way they start orbiting each other.)
I think larger mass stars tend to burn their fuel more quickly and thus die faster. Then again it's a large, weird universe out there. I'm sure a star orbiting an lower mass black hole has happened at least once.
If the star is more massive, i'd describe the black hole as orbiting the star. This matters as detecting such a situation would be more akin to detecting an invisible exoplanet than a fast-moving and bright star.
Depends on the size of the black hole. The Roche limit would require a ridiculously massive black hole or the star is broken up because the closest bits to the black hole are much more strongly attracted than the farthest bits.
how about a neutron star black hole binary of comparable mass? in that case you're dealing with a roche lobes instead of a more or less fixed roche limit that applies when one mass has a negligible fraction of the other.
For those like myself who struggle to understand these numbers, 1% of speed of light is like travelling the circumference of the Earth 75 times every second.
You're absolutely right - I did the calculation as km/s instead of m/s.
So at 1% of speed of light, it would take just over 14 seconds to travel the circumference of the Earth. Travelling at 1% of speed of light, I could travel from New Orleans to California in 1 second.
