Momentum-density is represented in the stress-energy tensor, and so is directly related to spacetime curvature. Light feels and generates gravity.

A sibling comment points out the hypothetical kugelblitz as an extreme example. In cosmology textbooks you can read about the "radiation-dominated era" of the first roughly 50000 years of the universe where the energy density working strongest against the expansion was dense photons (and neutrinos).

Observations of distant galaxies and the cosmic microwave background do match the (expanding vacuum) Lemaître-Robertson-Walker metric with the distribution of matter-density described by the Friedmann equations. Distant galaxies fill the sky and are receding from us, from our perspective; they are not concentrating in any sort of middle.

There is insufficient evidence to conclude that a big crunch is in our future.

"Pure energy" is represented in the stress-energy tensor just fine. General relativity's Einstein Field Equations exactly relates the stress-energy tensor to the curvature of spacetime. It gravitates, your argument just falls down.

<https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor#/...>

The black hole shadow for Schwarzschild and for Kerr are very different. The latter, which we expect for spinning black holes, is asymmetric and distorted depending on the direction to the observer (maximal for an observer in the equatorial plane, minimal for an observer above a pole).

Most astrophysical black holes have a lot of spin, mostly because their progenitors (stars, and smaller black holes formed by stellar collapse) have lots of spin. Infalling gas clouds tend to inspiral rather than fall straight in radially on one of the poles, and that also increases the BH's spin as it grows.

So, no, the shadows of most astrophysical black holes will not look like Schwarzschild.

You need a quadrupole for gravitational radiation. Blobs of gas and distant starlight generate a negligible quadrupole when they are near an isolated black hole. You get significant gravitational radiation when there's a quadrupole, which we can think of as a barbell: two heavy masses connected by an imaginary bar connecting them as they rotate around the barbell's centre of mass. (For extreme mass-ratios the centre of mass is inside one of the BHs, but for BHs of similar masses, it's near the middle of the "bar"). The gravitational radiation is because, if we think of the metric as reflecting a gravitational potential, that changes when the two items are eclipsing versus when they are spatially separated: you are attracted more strongly to the lined up configuration and will tend to fall more towards one or the other of the weights when they are not. Schwarzchild BHs are not barbell-like, and so don't emit gravitational waves.

There is so much noise around real black holes (even ones with a vanishingly small accretion structure; there's lots of background objects in our sky!) that there is little hope of directly observing a horizon-crossing, even if the gravitational redshift didn't lead to dimming etc. However, we have seen bright flares that are good evidence for parts of things (stars, for example) falling in.

Infallers are not smeared across the horizon. They are if anything asymptotically "frozen" in the distant observer's view. One could imagine a distant observer seeing a pile-up of objects, but the later ones will simply occlude the earlier infallers.

I dunno where you get smearing from. Complementarity or holography? That's about where (for a particular mathematically-related pair of equally valid descriptions) information is encoded for outside observers to reconstruct the BH's history, and not about a physical infaller's apparent location. (An infaller doesn't experience any of this itself, and would tend to prefer a local description of its fate, but not for long).

You need a gravitational quadrupole to emit gravitational radiation; in essence you need a "barbell" with an infinitesimally small "bar" connecting two large weights. (The weights can differ; the bar's length can change). Schwarzschild is characterized by a central mass, and so can emit no gravitational radiation. (One can do perturbative methods on Schwarzschild to introduce gravitatonal radiation; and in reverse the effective one-body formalism basically (over-simplified) turns a binary black hole with a large mass ratio into a test particle in a Schwarzschild background).

Additionally, there is the Vaiyda null dust absorbing metric, where "null dust" is very much like light. In this metric, the central mass grows, and the apparent horizon (where outgoing null rays turn inwards) is r = 2m(v), where v is the advanced time. That locally-defined dynamical surface moves outwards. There is also an event horizon in Vaiyda, but it is neither locally detectable nor coincident with the apparent horizon (that global null surface lies well outside during accretion).

That's the closest starting point to an answer for an isolated non-rotating black hole that grows by accretion; one can perturb Vaiyda with something more realistic than a constant "rain" of noninteracting massless (but not momentumless) particles.

That's just for monopole growth though. Like with Schwarzschild, Vaiyda is non-radiating (and in V's case this is by construction). An astrophysical isolated single black hole will see infalling material that has angular momentum; anisotropic stresses (beyond the null direction) (radiation from matter-matter interactions); a gravitational quadrupole (emitting gravitational radiation); and for big lumps of infalling material, some self-gravity.

In these cases, the black hole "shadow", the topic of the article at the top, reveals the details of the black hole, including growth. The shadow is fundamentally a gravitational lensing effect, and depends on the BH's mass, angular momentum, and charges. For a growing Vaidya black hole, the shadow is not static. The distant observer will see the shadow evolve in various ways. This is because it's a dark region whose boundary tracks the changing spacetime geometry. In the pure Schwarzschild case, the shadow is static, eternal, empty, and set by the boundary of the photon sphere at r = 3M rather (and rather bigger) than the event horizon at r = 2M.

For an astrophysical black hole, the observer's view of an infaller will be largely washed away by various sources of noise and the gravitational redshift of the infaller. However projects like the GRAVITY collaboration (at ESO's Very Large Telescope) look for infrared flares around Sgr A*, and have spotted really interesting things like the "G2" gas cloud. This is a busy area of current research. TDECat is a catalogue of more than a hundred tidal disruption events, mostly from X-ray flares and delayed infrared emissions from various space instruments. A lot of this is stuff actually falling into the black hole, but "covered" in a huge burst of high-energy radiation from real matter colliding together faster and faster as it inspirals.

Finally, we've seen the gravitational waves emitted by merging black holes of various mass-ratios. The result is a single bigger black hole and an enormous amount of gravitational radiation. The behaviour of matter near the merger and between the merger and us can corroborate that result. So we can see growth in that case, as well as where we can image a BH's shadow. These BHs are not very close to us. So clearly the idea that nobody can watch growth or consumption is wrong, although one might get nitpicky about which of these observables are indirect, but that's like saying that because Miss Marple sees only a bled-out corpse with lots of stab wounds there is no evidence that a murder has been committed.

Consider two strongly-interacting freefallers related by a boost colliding and sticking together (like a black tshirt and a floof of white pet fur) close to the apparent horizon.

Consider a freefaller and an accelerated observer meeting close to the apparent horizon. The freefaller here could be distant starlight and the accelerated observer a powerful rocket.

Are you saying these coincidences are forbidden in the vicinity of an apparent horizon (which is locally detectable), or are you distinguishing between the apparent horizon and the (global, but not locally detectable) event horizon?

Where is the point where the t-shirt will remain unsullied by unremovable fur? What light does an outwards-pointing camera on the spaceship see?

Visser [2014] "Physical observability of horizons", https://link.aps.org/doi/10.1103/PhysRevD.90.127502 aka https://arxiv.org/abs/1407.7295 about the variety of horizons about which one should be careful.

The equivalence principle demands that the local free-fall frames on the t-shirt and the fur are both smooth. At an enormous black hole, the curvature is also small (we can make the black hole so large that the curvature and tidal effects are comparable to the surface of the Earth). The result is the "no drama" conjecture, wherein nothing special happens immediately upon crossing the event horizon. Detecting the apparent horizon requires some cleverness to shear apart a cloud of coffee grinds or the like while the components are variously on hyperbolic trajectories (and will escape the region around black hole) and infalling trajectories (which will be stuck below a trapping surface).

The shirt-and-fur will form a single extended object and continue to infall togther. A violation of this would be a violation of Local Lorentz Invariance, which would be beyond known physics, all of which enjoys LLI (and global Lorentz Invariance in the idealized flat spacetime of Special Relativity).

This gets trickier just inside the horizon because of of causal disintegration: electromagnetic interactions from the inner part of an extended object can no longer reach up to the outer part of the extended object. For a time the outer part of the extended object can "catch up", but eventually intermolecular and other forces will fail, such that the tshirt will not experience being furry.

Local physics is local. The tshirt-fur meeting above the apparent horizon may be too redshifted to be visible by various classes of observer above. The electromagnetic radiation from them meeting below the apparent horizon is stuck behind a trapping surface; observers above will not see a furry tshirt.

Generically an accelerated freefaller shooting itself through a horizon will see freefallers as being fast (clocks running fast, high velocities). The effect increases as the horizon is approached, so a camera looking back at distant starlight sees a high blueshift and a focusing into a small region of the accelerated infaller's "sky". One can analyse this in several ways, but the acceleration/gravitation equivalence means the rocketing infaller is not much different from an observer standing still on a planet freely falling into the BH, or alternatively one can consider its suprageodesic in a convenient system of coordinates in a setting like Vaiyda's absorbing null dust. The inwards-accelerating rocket camera sees a blueshift from its own acceleration (because that is equivalent to gravitational blueshifting) and from the falling of the distant starlignt down to the black hole, which will be blueshifted in the backwards pointing camera.

Finally on the inwards-accelerating rocket, we have Unruh/Rindler in play locally (and local is fairly large for an enormous black hole); the Rindler horizon is ahead of them, so the backwards view is not behind the Rindler horizon. They can still receive light from outside. You don't want to collide with anything on an intersecting geodesic if you are this type of infaller, and eventually that includes highly-blueshifted starlight. Sizzle.

(In criminal law, "justice delayed is justice denied" and clarifications of constitutional or treaty requirements for speedy trials also can be tidied up by the legislature in a statute of limitations).

Statute (legislation) is a superior source of law to contract law, and so there is generally no way to contract to avoid being statute barred if a claim for breach of contract (or specific performance, etc.) is made beyond the statutory deadline.

Typically there are carve outs enacted in a statute of limitations that allow a claim to be brought out-of-time if the defendant has acted in a dishonest way that prevented a claim from being filed in time, for certain classes of litigant, or for certain types of claim. (And in criminal law, for certain offences - serious crimes will tend to have a longer, or no, limit on how long after the crime the prosecution is begun).

A statute of limitations typically does not extinguish defences based on the lapse of too much time; but such defences in some jurisdictions may be contracted away, leaving the statutory limit as the hard deadline.

Comments URL: https://news.ycombinator.com/item?id=49846158

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Four-velocity is defined on a timelike geodesic - its four functions take proper time as a parameter.

Proper time is a parametrization of a timelike geodesic which has several useful properties: it is monotonic allowing for orientability, and gives a unique real value for every infinitesimal point on the geodesic. This in turn means the tangent vector is preserved when parallel-transported along the proper-time-labelled timelike geodesic, with the gross physical meaning that the direction and speed of travel (in local forward/left/up coordinates for example [1]) does not change as proper time advances.

But we can label any curve -- or segment of a curve -- any way we want as coordinates are not physical. It's just that proper time is exceptionally useful as a coordinate. In particular, it satisfies the geodesic equation, gives us a four-velocity, which multiplied by the object's Lorentz-invariant mass gives us a four-momentum.

Unfortunately proper time is undefined on non-timelike geodesics, so can't be used for light, which in vacuum is always on a null geodesic.

However, there are functions that have the same features as proper time, namely monotonicity, uniqueness, and the preservation of the parallel-transported tangent vector. These are affine parametrizations. Proper time is an affine parametrization for timelike geodesics, and is usually denoted τ; null affine parametrizations which satisfy the geodesic equation are usually denoted λ.

We just can't use τ on null geodesics, since it is zero everywhere along one (so non-unique, and non-advancing). Statements based on the use of τ like "light experiences no time" or "light's path is infinitely length-contracted" improperly imply the use of τ.

However, if we use affine time λ, we get uniqueness, monotonicity, and the preservation of the tangent vector under parallel transport. The first derivative with respect to affine time at a point on the null geodesic lets us define a 4-momentum so we can use the Planck-Einstein relation E = pc = hf = hν = ħω relating the frequencies and wavelengths of photons, and how they redshift and dilate from point to point. (This is especially handy in curved spacetimes, like the expanding one in cosmology or the collapsing one around black holes).

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[1] An image may help: drop two dimensions from 3+1 spacetime to give us 2-space we get a tangent plane instead of a tangent volume at each point along a geodesic on a 2-sphere (which meridians on Earth's surface approximate) <https://en.wikipedia.org/wiki/Local_tangent_plane_coordinate...> -- sliding the tangent plane south along the meridian in uniform motion is like advancing the proper time.

> light never changes

is wrong. A photon has a momentum, which can increase or decrease as it travels through free space.

Using general relativity, it's straightforward to define an affine time on a null geodesic (even if one cannot define a proper time on one), and a momentum that is a function of the affine time at each point.

The Lyman-alpha forest is a straightforward "laboratory" for this approach, which can calculate the Lyα absorption lines seen when a bright distant quasar or luminous Lyα emitter has atomic hydrogen clouds between the distant source and us (the absorption lines indicate photons with a very narrow range of momenta participated in hydrogen atoms' electrons transitioning from ground to the first excited state, with the later relaxation photons radiating in random directions). The pattern of such dark spectral lines tells us how redshifted the background light and earlier absorption lines are at each gas cloud along the way.

https://www.astro.ucla.edu/~wright/Lyman-alpha-forest.html

https://en.wikipedia.org/wiki/Lyman-alpha_emitter

And over much-shorter-than-cosmological distances, https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment

> it really got me to think about this stuff.

Thank you, that is very generous of you to say.

This is how the academic dialogue works, and it dates back to early durable records in the ancient world -- about as far before Plato as Plato's Academy is before today's universities. Innovations like academic journals come from "merely" four centuries ago, and pre-publication evaluation by peers about three hundred years ago. Anonymized pre-publication review is more recent still, and publishing schedules (as well as the needs of the submitter to have the submitted work dealt with in good time) don't admit a dialogue over some subtle point a referee takes some issue with. Moreover, such a pre-publication dialogue is generally non-public, and often also filtered through an editor. It can get messy [1].

As I'm sure you've discovered in your own post-secondary education, academia is very conservative (in the sense of "retaining what mostly works, even in the face of mounting scaling problems", foremost among those being the ever-increasing volume of publishable works generated by researchers).

Your own idea is quite conservative, and has been tried from time to time. Direct compensation by journals of referees for their time has been the subject of rigorous human experimentation: https://10.1097/CCM.0000000000006637 https://www.biorxiv.org/content/10.1101/2025.03.18.644032v1 as recent examples, with mixed results.

Direct compensation of referees by journals has a number of pitfalls ranging from the fiddly details of how to deal with income tax liability pay (and credits towards future publication fees, etc) incurs to whether it compromises the objectivity of pre-publication evaluation (which is frankly already not very good in highly specialized areas).

Payment of reviewers by paper submitters is imho an even worse idea -- how do you preserve the anonymity of referees (especially with respect to the submitters)? Do submitters or reviewers have exposure to their (probably different) tax authorities for these transactions? (I can think of at least four national tax agencies that would view the received pay as taxable income, and also potentially subject to value-added tax on professional services. One already sees this problem with conference honoraria.)

Another -- one that already exists in the real world -- might be for institutions and grant-funders to build in support for peer review of others' work by project members. To the extent that detailed pre-publication review benefits academia, and societies that fund academia, as a whole, maybe referees should be rewarded (or even obliged) to do paid reviewing duty. One might compare the requirement to do pro bono work imposed on many practising lawyers by their regulating authorities (especially interesting are jurisdictions in which a party losing a court contest to a party represented pro bono usually must pay into a fund that supports the overall scheme).

Personally I think it would be more useful to everyone to have a solid reply paper published in due course than a blocked initial publication. My ideal is that referees aim to help submitters not accidentally professionally embarrass themselves.

Then on your reproduction idée fixe, supporting the generation of papers which confirm reproduction is something that societies could certainly work on. Many incentives to write and submit papers calling out flaws in others' work already exist, and of course could be expanded. I don't think any of that should be done with masking of the participants. Additionally, reproduction of results is often less interesting than (sometimes much) later testing of published results in significantly different ways.

(Indeed, foundational papers from more than ninety years ago are often re-proven by modern-day experiments, both as a side effect of (or opportunity arising from) pursuing the primary research goal, and as a way of testing e.g. new metrology technology, new computational tools, mathematical advances, and so on. Also, some of those foundational papers simply could not be tested with great accuracy with tools existing at the time of publication. Their publication, however, tended to drive the development of such tools, and in modern days such foundational papers are found to be good only within certain limits that could not have been explored closer to the time of publication.)

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[1] https://theconversation.com/hate-the-peer-review-process-ein... (2014)

Peer reviewers don't generally reproduce the work in the publications they are asked to review, at least not during the review process itself. Neither do journal editors.

If you want a real vanity press, check vixra and its origin story.

ArXiv does have moderators and endorsers in each area, although they are usually light-touch, weeding out literally unreadable submissions, ones that so obviously ignore formatting guidelines that it beggars belief they could comply with a typical journal's rules, and ones that are clearly submitted to the wrong area.

If anything, I think sometimes the net is too fine. Will Kinney just this week had a version of <https://www.acsu.buffalo.edu/~whkinney/SpecialRelativityBoot...> rejected by the arXiv, for example. The reasons for arXiv-rejection can be opaque.

Having a stable document early (a pre-print) tends to widen the scrutiny of papers that may ultimately be published to a journal whose editor's expertise lies in a very different area from the submission; this can and does lead to author corrections being made before journal publication.

There are plenty of peer-reviewed papers which are hot garbage that have found their way into prestigious high-impact journals like Nature and Science (see <https://retractionwatch.com/the-retraction-watch-leaderboard...> for examples, and note none of the top 10 are in areas covered by the arXiv).

> being published by a famous professor from a prestigious university is also no guarantee

Everyone in academia knows this, including the vast majority of famous professors from prestigious universities, because of online repositories like <https://retractionwatch.com/retractions-by-nobel-prize-winne...> (and much more sadly because of <https://en.wikipedia.org/wiki/Nobel_disease>, lower-profile versions of which academic paper-writers -- and dissertation writers -- tend to encounter as they chase the history of the problem before them or read late citations to works they are relying upon). This particular part of your set of claims is is not a real problem in academia or with the arXiv in particular.

Finally, what value does publication in a predatory journal bring? Do you believe that peer review and editing were actually even performed in the majority of MDPI's most predatory journals, for example? <https://www.predatoryjournals.org/news/list-of-all-mdpi-pred...> Some papers published in some of their pay-for-publication open access journals don't even get submitted to the arXiv; one might hope this is out of embarrassment by the authors, although the (low) bar set by the arXiv itself is certainly a factor.

The remedy for a reasonably argued but wrong academic paper isn't lack of publication, failed peer review, or editorial alteration, but rather reply papers. That's the academic dialogue.

Ethan Siegal (a former theoretical cosmologist who has lots of practice in his second career doing science outreach) did it well enough at a pop-sci level that I'll just point to his https://bigthink.com/starts-with-a-bang/what-universe-expand...

(I don't think I could do better [*]).

Here's a sketch for a crash syllabus that would take you closer to an answer I'd write, not being a practiced science communicator:

My approach would be to teach you some differential geometry on a differentiable Euclidean plane (mostly relating the classic Euclidean distance to the integration of a line element), then what a Riemann manifold is, then how a 3+1-d pseudo-Riemannian one differs from a 4-d Riemannian manifold (and understanding the Ricci curvature in an Einstein manifold), and take you to understanding the simplest of metrics on the Lorentzian manifold, and the concept of geodesics and how they separate into spacelike, timelike, and null. I'd also teach you early about affine distance so that you don't stumble into problems understanding that a pulse of light from the ground to a mirror on the moon and back to the ground takes about two seconds, and how a pulse of matter -- including a pulse of light -- loses energy in an expanding spacetime. (That's another where does it go question, and a good one to think about.) Then I'd introduce Raychaudri-equation-style thinking, with a spray of timelike geodesics separating, as a way of understanding the metric expansion of space and the FLRW metric (where each Friedmann-equation dust represents an enormous number of timelike and lightlike geodesics).

I'd also teach you about the Lagrangian and Eulerian specifications of the flow field, and how they relate to one another. We can have a idealized (freely-falling, feels-no-forces) Lagrangian observer follow one line in a spray of geodesics which are initially extremely close to each other, and which separate with the metric expansion of space. Some of the initially-close geodesics causally disconnect from our chosen Lagrangian observer, with close-but-less-close ones disconnecting quickly, and very-close ones staying practically parallel for a very very long time. This is basically the Raychaudri equation, as applied to cosmology. We'd want to explore radar distances between our Lagrangian observer and ideal reflective objects attached to other geodesics on the spray.

We then can relate all that to a spacetime-slicing approach where we track what's on 3-d spacelike hypersurfaces, in a Eulerian style, going from our Rachaudhrian spray to a collection of space-filling dusts or fluids that dilute away differently over time. This is the usual picture cosmology students operate with.

Understanding that, especially how expansion generates several cosmological horizons, is half of the key to answering your question. The other half is understanding that one can run the relevant equations under a time-reversal, with initially enormously distant objects freely falling towards each other and ending up practically on top of each other in the early history of expansion.

Along the way we'd also be talking about the thermodynamics, as expansion is adiabatic.

Our causal physics are all related to an extremely hot, extremely dense, extremely low-entropy volume in our billions-of-years-ago past, which we retrodict by studying fractions of later volumes (fractions as small as careful laboratory experiments and as big as large scale galaxy surveys). Anything close to that patch causally disconnected from us very early, and we'll never be able to hear from those parts of a big spray, and they'll never hear from us.

Just outside our very early universe, things probably look very similar to things just outside it. The logic here is that as our galaxy crosses out of a cosmic horizon of somone far away, our galaxy doesn't do anything weird, and likewise there are many galaxies currently crossing out of our cosmic horizons, and they probably aren't doing anything weird either.

Studies of the expansion history, still-viable cosmic inflation scenarios, and global spatial curvature have led to estimates (e.g. Guth's work) that some our early hot dense patch is at most 10^-23 of basically the same early hot dense stuff. That's fairly comparable to the number of atoms of water in the North Atlantic ocean, all of which are interchangeable, although they all have different histories of where they've been in Earth's oceans, the pressures and densities they've experienced on their travels, and so on. The pre-inflationary patch's tiny elements are pretty interchangeable although they'll have slightly different histories of expansion, galaxy formation, and so on, given tiny differences in their very early histories ("initial conditions"). Some may be overdense and quickly collapse. Some may be underdense and thus produce few if any stars.

Now, is that primordial hot dense patch embedded into something bigger? Good question! Does it even matter, given that it causally decoupled from us so early? Good question! How do we even begin to investigate that? Good question! That's all live postgrad and postdoc research, with a lot of focus on trying to make the low entropy part of our hot dense early universe seem un-special.

Siegel again: https://bigthink.com/starts-with-a-bang/cosmic-inflation-pas...

Once you have that under your belt you can join the manifold (pardon the pun) papers exploring the physical implications of various guesses about what's outside the everything-everywhere-everywhen fully determined ("block universe") picture painted by a notional exact solution of the Einstein Field Equations of General Relativity, which we can only successively approximate by sampling signals from our past.

But at least you'd then understand what it means to say that mean energy-densities fall over cosmological time, and that the centres of mass of galaxy clusters are separating over cosmological time, and that our distant distant descendants won't see any galaxies not presently in our local group.

For extra credit you could play around with embeddings of de Sitter space in higher-dimensional manifolds and run into the usual frustrations of it being quite hard to recover known physics -- one can even largely justify a statement like embedding a 3+1d spacetime into a higher dimensional spacetime is generally not possible. Of course, many people still attempt to make that work not so much to answer your question, but to find ways of more easily calculating the way our visible universe behaves.

[*] I'd have maybe said "its own future" and otherwise present a wordier version of what Siegel wrote (explicitly raising time-orientability), but really I'd want to explain why I'm mostly a blockworlder in spite of how us small temporary knots of atomic nuclei feel about that <https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time...> and that maybe the real question is why our brains encode the concept of expansion at all. Anyway our puny brains can't hold all knowledge, we can't just pour in mathematical physicslike kung fu, helicopter piloting, or motorcycle-hotwiring skills in The Matrix movies, and the behaviour of the universe at scales of billions of lightyears didn't change once humans started printing cosmology textbooks. And it's OK if you haven't worked through any of those; just be careful of memorizing factoids from people who haven't worked through any of them either.

Some exotic spacetimes involving pp-wave sandwiches can focus initially non-converging and spatially distant light pencils onto each other at a caustic shortly after the passing of the stack of plane-parallel gravitational waves. One can hide some such processes in the early cosmos.

Comments URL: https://news.ycombinator.com/item?id=49437210

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Comments URL: https://news.ycombinator.com/item?id=49405646

Points: 8

# Comments: 1

We should also remember the enormous cosmological curvature in which testable quantum systems exist; it's not just about compact objects. Significant? There's observed H-sources above z ~ 15, and of course the CMB photons at z ~ 1100. Indeed, B&D deals with Robertson-Walker spacetimes over several chapters before they get to black holes.

Also at the weak but measurable curvature regime there's e.g. Pound-Rebka, time metrology[1], and so forth, and lots of spacecraft confirming the strong equivalence principle (e.g. MESSENGER, LAGEOS) and thus supporting the LLI one expects to find in relativistic QFTs of the sort one would use to describe the behaviour of laser altimeters, distant astrophysical masers (and the Lyman-alpha forest), the spectral lines in stellar atmospheres and so on.

[1] just because it's neat and directly relevant to your comment: https://journals.aps.org/prxquantum/abstract/10.1103/q188-b1... [2025]

Comments URL: https://news.ycombinator.com/item?id=48526020

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