Light can be deflected by a large angle if it passes close enough to a black hole. In principle, light from a star on one side of the sky could indeed be deflected toward us by a black hole on the other side of the sky. See for example this simulated picture and notice how the galactic center on the right-hand side of the picture also appears to the left of the black hole, within the Einstein ring.

However, there is no concern that this effect could lead to seeing stars in the wrong places. As you can see in the picture, the black hole makes a distorted image of the whole sky. If we were able to resolve an individual star in that image, we would certainly also resolve the whole distorted image of the sky and infer that a black hole is there.

Anything inside the event horizon must reach the singularity in finite proper time (that is, time from its own point of view). However, events inside the horizon can never be in the (causal) past of an outside observer, so there is never a time at which an outside observer could say objectively that the neutron star is no longer there. Maybe that's what the claim was?

To the extent our current best theory of gravity (general relativity) is accurate, it is not possible for a static extended structure to exist inside the event horizon of a black hole. Gravity there is so strong that even outgoing photons move toward the center; that's why there's an event horizon. If a static structure existed, its material would have to move outward faster than light, which is impossible.

Also: > As the mass rises for a neutron star, it reaches a point where that mass at that diameter no longer allow light to escape the surface.

This would happen for an idealized rigid body, but it's not really what happens to a neutron star. As the neutron star's mass rises, the repulsive interaction between neutrons is no longer able to support the star against gravity, and it collapses (see the TOV limit). That's when the black hole forms.

(If a neutron star could maintain its structure up until the event horizon enveloped it, the maximum mass of a neutron star would be at least 4 solar masses. Instead it's 2-3 solar masses.)

That's a fair suggestion. I'll make sure to include mention of dark energy next time.

I'm addressing expansion of space because that's the topic of the question. I am confused as to why you think I should answer a different question.

(Regardless, it would seem to me that the appropriate course for you would be to make a separate answer, rather than to falsely claim that the existing answer is incorrect!)

Dark energy's gravity accelerates cosmic expansion. Dark energy also induces small-scale gravitational repulsion. However, we cannot say that cosmic expansion induces small-scale gravitational repulsion, because the two are not directly linked.

That is the claim in the top-level comment: that cosmic expansion does not have a local dynamical influence. This claim remains correct.

The repulsive force acting at small scales is not linked to the cosmic expansion rate, as detailed in other replies. It is highly misleading to attribute it to the "expansion of space". It's just gravitational repulsion arising from the (stress-)energy density of dark energy.

It's fine to view space as expanding, since again, that represents a convenient coordinate choice. I use it frequently in calculations. The key point is just that this "expanding space" doesn't have physical consequences.

It's like how two people walking due north from the south pole will gradually separate from each other despite walking in the same cardinal direction, but the process of walking north doesn't induce an expansion force on your body.

Sure it would. Imagine that a bunch of particles all explode outward from a point at different speeds. The ones moving fastest will end up farthest, and you automatically end up with a picture where recession speed is proportional to distance.

> For example, if “space was expanding” except for things that are close enough overpower it with gravity, how would that result be different from dark energy creating a repulsive force except for things that are close enough to overpower it with gravity?

The main problem is that dark energy's repulsion has no intrinsic link to the global expansion of the universe. For example, as I noted in another comment, in Einstein's static universe (in which matter's attraction balances dark energy's repulsion), there is a repulsive force even though the universe is not expanding.

More generally, the repulsion from dark energy has no link to the cosmic expansion rate at a given instant. It does connect to the rate of change of the cosmic expansion rate (i.e. the acceleration), but this link is only partial, since dark energy is only one of the factors controlling the rate of cosmic acceleration (the other main one being matter, which decelerates expansion).

> Also, how can galaxies be “carried by their initial momentum” as you confirmed above AND all be moving away from one another at the same time. Maybe I’m misunderstanding something but that doesn’t really make sense. The only way all galaxies that are not locally bound to one another could be moving away from one another is if that space between them is somehow expanding, similar to the “dots on the surface of a balloon” metaphor that is often used. If we instead imagine an “initial momentum” scenario, it suggests a single point of origin in space, similar to an explosion. But in the case of an explosion, there is a center source, which the universe doesn’t appear to have.

The universe can originate from a single point in spacetime while still having no center in space. Due to the principle of relativity, any observer departing from that point has an equally good reference frame, so there is no way to decide that one observer is better than another.

(You could still suggest defining the center in terms of "distance from the edge". There doesn't have to be an edge, though.)

> Also, the red-shifting caused by an explosion would not be so uniform, but have many items moving away at much faster speeds than others relative to the observer.

That's not a fundamental limitation, it's just intuition from the explosions you know. The initial "explosion" doesn't have to be messy (for example if it arose from inflation). Also note that in an expanding system, velocities self-sort because if an object is moving rapidly with respect to the material near it, it's not going to stay near that material. Instead it will gradually end up near material moving at the same speed. (This effect is essentially the cosmological redshift applied to massive particles.)

Odd, I'm not sure why they cite that there. But the error made in the Cooperstock et al. article is pretty elementary, in any event. By starting with the FLRW metric for an Einstein-de Sitter universe, they assume from the outset that matter is homogeneously distributed everywhere at the critical density. The force that they claim arises from the expansion of the universe is really just the gravitational influence of this matter.

That happens only if dark energy is phantom energy, which is not really supported by observations or theory, but can't be definitely ruled out either. Essentially what happens is that in these models, the pressure of the dark energy fluid is sufficiently negative that expansion raises its energy density. With higher energy density, its gravitational repulsion becomes stronger. Eventually the repulsion becomes strong enough to separate atoms.

Within the framework of general relativity, dark energy induces gravitational repulsion, which essentially accelerates everything away from everything else. That means it accelerates cosmic expansion.

While this repulsion is sometimes framed as a consequence of accelerating expansion, it doesn't really make sense to put the causation in that direction. For example, in Einstein's static universe, there is repulsion, even though the universe is static (because the repulsion balances matter's attractive gravity). It's really just gravitational repulsion arising from the energy density of dark energy (or the cosmological constant).

> That sounds plausible. So to further and solidify my understanding, space itself is not expanding, just that physical entities (e.g. galaxies and therelike) are moving apart carried by their initial momentum.

Exactly.

> But what I don't quite understand is the notion that this expansion (or motion) seems to accelerate relatively to each other, to a point where distant objects become unreachable for us even with we could travel at the speed of light. Or am I mixing things up here?

Dark energy induces gravitational repulsion, which accelerates the expansion of the universe and also creates a cosmological event horizon. Indeed the mathematics are very similar to that of a black hole, but inverted, so that whereas things too close to a black hole cannot escape, with dark energy, things that are too distant (with respect to any observer) cannot return. (When thinking about unreachable distant objects, it is we who have become too distant from the object.)

First, let me emphasize that expanding space is not a physical phenomenon. It's a common misconception that there is something like the fabric of space, which expands over time, stretching out systems and carrying objects with it. Expanding space is just a convention that simplifies some of the mathematics in cosmological contexts. It represents a choice of coordinates on spacetime. It is not a physical process.

Since the idea of expanding space is a tenacious misconception, I've put a great deal of further reading at the bottom of this post.

That being said, the universe is expanding, and that means that objects are moving apart in a fairly uniform way, on average. At the largest scales, this expansion seems to be about the same everywhere (homogeneous) and the same in every direction (isotropic), but this is certainly not true at smaller scales. For cosmic voids -- regions less dense than the cosmological average -- their expansion has been slowed less by gravity than the universe at large, so they are expanding faster than average. Conversely, regions that are denser than average expand more slowly, due to their higher self-gravity, and they can even stop expanding and collapse. This collapse process is how galaxies are formed. Galaxies themselves consist of stably orbiting material and hence are not expanding or contracting (except to the extent that they are disturbed by newly accreted material).

Asymmetry in a system and its environment can also exert a tidal influence, which basically means that gravitational forces are different in different directions. This can cause the system to expand at a different rate in different directions, resulting in structures like filaments and sheets in the large-scale structure of the universe.

Regarding expanding space not being a physical influence, see for example this entry in the AskScience FAQ. If you prefer to hear it from eminent cosmologists, here is an excerpt from a 1993 interview with Steven Weinberg and Martin Rees:

> Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?

> ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’

> Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept,’ he says. ‘Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.’

> Narlikar puts it differently. ‘Space is not utterly empty: it has visible matter in the form of galaxies and also a lot of dark matter.’ Weinberg elaborates further. ‘If you sit on a galaxy and wait for your ruler to expand,’ he says, ‘you’ll have a long wait – it’s not going to happen. Even our Galaxy doesn’t expand. You shouldn’t think of galaxies as being pulled apart by some kind of expanding space. Rather, the galaxies are simply rushing apart in the way that any cloud of particles will rush apart if they are set in motion away from each other.’ The matter inside individual galaxies does not take part in the general expansion because it is held together by gravity.

Beyond these, here are articles discussing the point further:

(1) A diatribe on expanding space. This is pretty technical, but it's the most direct attack on the idea of expanding space. One key quote is that

> there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost.

If a system is not expanding, then cosmic expansion is simply not relevant to it.

(2) The kinematic origin of the cosmological redshift. Very well written and less technical, although there are mathematical arguments. The main point of this article is that the cosmological redshift -- often framed as a consequence of space expanding -- is more directly just a Doppler shift. One of the introductory paragraphs reads:

> A student presented with the stretching-of-space description of the redshift cannot be faulted for concluding, incorrectly, that hydrogen atoms, the Solar System, and the Milky Way Galaxy must all constantly “resist the temptation” to expand along with the universe. One way to see that this belief is in error is to consider the problem sometimes known as the “tethered galaxy problem,” in which a galaxy is tethered to the Milky Way, forcing the distance between the two to remain constant. When the tether is cut, does the galaxy join up with the Hubble flow and start to recede due to the expansion of the universe? The intuition that says that objects suffer from a temptation to be swept up in the expansion of the universe will lead to an affirmative answer, but the truth is the reverse: unless there is a large cosmological constant and the galaxy’s distance is comparable to the Hubble length, the galaxy falls toward us. Similarly, it is commonly believed that the Solar System has a very slight tendency to expand due to the Hubble expansion (although this tendency is generally thought to be negligible in practice). Again, explicit calculation shows this belief not to be correct. The tendency to expand due to the stretching of space is nonexistent, not merely negligible.

(3) On The Relativity of Redshifts: Does Space Really "Expand"? The least technical of the batch, this article is also focused on the interpretation of the cosmological redshift. It includes the choice paragraph:

> While it may seem that railing against the concept of expanding space is somewhat petty, it is actually important to set the scene straight, especially for novices in cosmology. One of the important aspects in growing as a physicist is to develop an intuition, an intuition that can guide you on what to expect from the complex equation under your fingers. But if you [are] assuming that expanding space is something physical, something like a river carrying distant observers along as the universe expands, the consequence of this when considering the motions of objects in the universe will lead to radically incorrect results.

The answer is time dilation, essentially. Even though our spacetime is globally curved, it's more intuitive to think about a flat spacetime, since that removes ambiguity about the definitions of distances and relative velocities. In this scenario, the most distant objects are receding at velocities arbitrarily close to the speed of light. That means that even though they might have traveled a great distance from their origin point, arbitrarily little time has passed for them, due to time dilation. So we can receive light from these objects that tells us the state of the universe at arbitrarily early times, even though they could be quite distant from the origin point for the universe.

(I'll also note that a common answer to this question is that the universe didn't begin at a point. While that would also resolve the problem, it's not something we can say for certain.)

> Space is a real thing that can expand. If you’ve heard phrases like “the fabric of spacetime” or “the spacetime continuum”, these are actually real, not just some sci-fi mumbo jumbo. You can imagine a big rubber sheet, on which all the planets and stars and everything are sitting. If you label this sheet with a grid and stretch it out, you’ll see that stuff gets further apart, but it doesn’t change position on the grid. That’s how space expands: it doesn’t move things, it just makes the distance between them bigger. (Note: don’t take this analogy too far: unlike rubber, space can stretch infinitely, and it doesn’t “snap back” into place).

This is kind of a problematic way of thinking, because there isn't any objective sense in which space or spacetime can move or stretch. Those kinds of effects only ever represent subjective choices, often made to simplify a mathematical problem. They are coordinate choices, specifically. The only objective property of a point in spacetime is its (tensor) curvature.

For example, the idea of space expanding is a coordinate choice. It's equally valid to just say that objects are moving apart.

(How, then, can things recede "faster than light"? Just as it's not possible to uniquely define the angle between arrows drawn at different places on a curved sheet, relative velocities of distant objects in curved spacetimes are not meaningful.)

The Planck 2018 paper gives 13.787 ± 0.020 billion years, so that's an uncertainty of 20 million years. That's from the cosmic microwave background.

However, supernova-based measurements of cosmic expansion favor about a 7% higher expansion rate, which could imply the universe is younger by of order a billion years. This discrepancy is the "Hubble tension", a major current research topic.

It's only isotropic (the same in every direction) if you're in the CMB rest frame. Otherwise, due to the Doppler effect, one direction will be blueshifted and the other redshifted.

Gravitational time dilation is at most of order one part in a million in most contexts. It's only significantly larger near black holes, neutron stars, and white dwarfs.

I'll first note that when thinking about the possible trajectories that reach a given spacetime point (e.g. earth in 2023), there is a trajectory that maximizes the elapsed time since the beginning of the universe.

Does that trajectory correspond to the CMB frame? If the universe is homogeneous, then yes. In the presence of peculiar gravitational fields, like those of our galaxy, that doesn't generally remain true, although I think you could pick a "time threading" such that it does. That's another gauge freedom I didn't mention. Along with the freedom to pick the "different positions at the same time" surfaces in spacetime, there's also freedom to pick the "same position at different time" lines.

This is a good way to think of entanglement, as long as you also keep in mind that not every configuration of entangled particles corresponds to a set of local hidden variables in this way (those would be the spooky outcomes you're referring to). But most entanglement scenarios people think of are indeed equivalent to local hidden variables.

An individual photon doesn't have a rest frame, but the CMB rest frame is the center-of-momentum frame of a collection of photons. Since the photons have all different momenta, their center of momentum doesn't move at the speed of light.

Gravitational time dilation, due to the -(1+2Φ)dt^2 term in the metric. (In synchronous gauge, that term is just -dt^(2)). The result is that the elapsed time is shortened by a factor of about 1-Φ, where Φ is the Newtonian gravitational potential, of order 10^-6 in our galaxy.

A billion years off is likely possible, given the Hubble tension. There's about a 7% difference between the present-day expansion rate favored by the CMB (~68 km/s/Mpc) and the present-day expansion rate favored by supernovae (~73 km/s/Mpc). 7% of 13.7 billion years is a billion years.