Newtonian gravity gives infinite time to fall into black hole?

I thought you need at least special relativity for time dilution.

Both have finite time falling in to the singularity. If you use a point test particle Newton and GR agree on that finite time.

That's proper time I.e. the infalling particles wristwatch time.

In GR, external observers would never see the infalling particle cross the event horizon but that's a coordinate artifact. If using our wrist watch time for that particle.

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gradus_ad 9 hours ago | parent | next [-]

But observers can see a black hole grow over time, so does that mean they observe growth without consumption?

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rustyhancock 9 hours ago | parent | next [-]

Were past what I could confidently answer (if I'm wrong hopefully someone corrects me) but I'm not sure I follow, if the BH grows it would encompass what we see as nearly smeared over it's horizon.

There's also surprising results around what the external gravitation field appears to be for an object.

I.e. no matter how mass is distributed behind the event horizon externally it looks like the spherically symmetric Schwartzchild metric.

That has implications for what will emit gravitational waves.

Eithway, smeared over the horizon but never crossed and crossed the horizon externally look the same from a gravity perspective.

	▲	raattgift 7 hours ago \| parent [-]
		The quanta article at the top is about BH shadows. 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).

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raattgift 8 hours ago | parent | prev [-]

Merging astrophysical ("real world") black holes are quite different from the idealization in the Schwarzschild setting.

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.

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raattgift 8 hours ago | parent | prev [-]

> external observers would never

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.