A black hole is a creature of pure self-sustaining curvature — the field itself has enough energy in it to maintain the warpage (as the singularity presumably at the core is beyond the event horizon and gravity, like everything else, cannot escape it’s own grip and emanate from the singularity to the event horizon where we observe the effects).
So tossing in antimatter would not do much. It would never cross the horizon in an external observer’s reference frame and thus would never interact with anything and thus would produce no effects.
Besides we know that when matter and antimatter react, they emit energy that has positive sign, not zero... twice the value of any particle’s mass. That in turn implies that matter and antimatter have the same sign of energy despite opposite charge.
Furthermore by coupling attractive matter and repulsive antimatter one could create a perpetually-accelerating device as the repulsive antimatter would try to escape the matter and the matter would chase after it. This obviously is cause for concern (but in general General Relativity does not conserve energy, so it’s not incompatible with the theory per se — just very dubious).
I’m expecting the antimatter to fall downwards just as matter would. But the whole point of science is to check that what you expect conforms to what the universe actually does. So this is definitely not a waste of resources: much the contrary, it’s a vitally important measurement to make.
I don't this is exactly accurate. Hawking radiation for example, causes black holes to evaporate over time. While the radiation that is detected outside the black hole has positive mass/energy the in-falling anti-particles have negative mass/energy which results in the net reduction of the black hole's mass/size. Does it not then make sense that in-falling anti-matter would have an evaporating effect?
The “one of the virtual particles of the pair created in the vicinity of the black hole’s horizon falling in leaving the other one to escape to infinity as radiation whose mass-energy must be subtracted from that of the black hole” view of Hawking radiation is a pedagogical construct thought up by Hawking himself after calculating the effect by other means for the sake of public promulgation. In reality it has to do with the restriction of the resonant modes of quantum fields imposed by having a border (horizon). Case in point: if the full truth were that of infalling versus escaping virtual particles there’d be a definite trajectory associated with the escaping particle that would convey information about where, approximately, the virtual particle/antiparticle pair popped into existence, violating Heisenberg uncertainty. In reality, Hawking radiation has wavelengths comparable to the diameter of the black hole that make it impossible even in theory to resolve where the supposed particle/antiparticle pair “popped” into existence, preserving the uncertainty principle. This is also why radiation becomes more energetic as the hole shrinks in size: that’s because the associated diameter shrinks and allows wavelengths of emitted radiation to contract, packing more energy into those waves. If it really were particle/antiparticle being shorn apart by the hole’s gravitational attraction you’d expect more radiation to be emitted by a big hole (vacuum activity per volume area being constant, and thus a bigger hole would border more unit volumes and allow for greater interaction with the quantum vacuum that would slow down as it shrank).
Hang on, Heisenberg's uncertainty principle doesn't need to be preserved with virtual particle/anti-particle pairs - that's the point of Hawking radiation - the particles are no longer virtual, and so much must acquire a real value of energy from somewhere (and do so from the mass energy of the black-hole).
You're very much trying to draw a line here that QM doesn't support - everything is a particle and a wave at the same time, and the interpretation that one pair of a particle in-falls is at least as valid as the interpretation that it's to do with the exclusion of wavelengths.
EDIT: For example, the proposed argument with bigger black holes falls down by a similar interpretation to the wavelengths - for virtual particle pairs with sufficient initial velocity to escape the gravity of the black hole, the initial location of them by necessity becomes very indeterminate, or their mass very light - in both cases making it progressively less likely with black hole size that one part of the pair appears initially inside the black hole event horizon, or makes the resulting energy of the radiation less and less.
No, it was in his 1975 work [1], which considers a non-interacting quantum field in a Schwarzschild black hole spacetime [2]. The negative energy infallers keep the spacetime static, which is handy for preserving a timelike Killing vector field that is orthogonal to the spacelike hypersurfaces at each Schwarzschild time coordinate. That picture made it straightforward to show the mechanism for evaporation; perturbing the picture does not make Hawking radiation vanish, but does make it much harder to calculate.
> sake of public promulgation
It [1] was a hard academic paper aimed at experts. That should be abundantly clear not far down its first page and certainly by its second.
> restriction of the resonant modes of quantum fields imposed by having a border
It has to do with vacuum states.
> the [bh] shrinks and allows wavelengths of emitted radiation to contract
I think you run into controversy (and indeed a bit of inconsistency in your "true picture" argument) with "emitted". There is a secondary issue surrounding gravitational time dilation, depending on where you think Hawking quanta are found.
> Heisenberg uncertainty
How does that enter into the (non-string) picture except at the latest times when the radius of curvature is on the order of Planck length? I'm genuinely curious to see how you'd use Heisenberg uncertainty except in an argument involving remnants (in which a generalization of HUP could dynamically prevent complete evaporation, with the dynamics becoming important at some small minimum BH mass).
Anyway, I strongly recommend Wald [in [2]] to you.
[2] It's hard to summarize this better than Wald in the Hawking Radiation section of https://dx.doi.org/10.12942%2Flrr-2001-6 notably starting with 'The original derivations [54, 98] made use of notions of "particles propagating into the black hole", ...' and I don't want to plagiarize him.
Hawking radiation is a pure hypothesis based on one particular assumption how thermodynamics and quantum mechanics can be applied to gravity. We have no evidence that it exists. If one follows a different school of thought, then the temperature of the event horizon of the black hole is zero and there is no radiation.
> Does it not then make sense that in-falling anti-matter would have an evaporating effect
Yes, kinda. More precisely, it would depend on how anti-gravitation works exactly, i.e., how anti-matter couples to gravity differently from matter. So even more precisely, "we don't know but can model various remotely plausible ideas with current theory" [a concrete attempt to model below at [1]].
One approach to model anti-matter anti-gravitation is to have a second metric which anti-matter feels but matter doesn't. Bimetric theories have been studied for several decades, and the problem is that one has to hide the effects of the second metric or we get a very different night sky than we observe. So while bimetric theories aren't ruled out, the effect today (as opposed to the very early universe) is extremely small. A tiny present-day effect would be interesting in that it would suggest a possible mechanism for the overwhelming dominance of matter in our part of the universe: a decaying secondary metric could strongly segregate matter from antimatter in the very early universe (preferentially collapsing matter together with other matter, and antimatter together with other antimatter), while not interfering with today's observations of high-redshift galaxies or laboratory experiments to date.
In a bimetric setup, a black hole would source something akin to Schwarzschild for the dominant metric, and something akin to anti-Schwarzschild (for matter) as a secondary metric. We could contrive a secondary metric that causes antimatter produced in the hot accretion disc to receive a dynamical boost that transfers extra energy-momentum into the antimatter and flings it off towards infinity. In that case, anti-matter that anti-gravitates would have an evaporative effect on the black hole.
There is of course no observational evidence favouring a strong secondary metric anywhere in the known universe, and it would be an awesome surprise if forthcoming black hole telescopy found any. Meanwhile people are working on ruling out a weak secondary metric in laboratory settings.
There are other approaches to theoretical modelling of anti-gravitating anti-matter, but they generally need a dynamical suppression of the effect at modern times and large mass scales, for the same reasons. Such approaches typically look really highly contrived on their faces, and of course suffer from lack of evidence, since we don't have a good view (with current technology) of the universe before the cosmic microwave background formed.
We can be pretty sure that anti-matter doesn't anti-gravitate at all from nuclear physics (electron anti-neutrinos in beta decay, and the antiquark halves of mesons) in astrophysical observations (you get a lot of both in supernovae (SN), and anti-gravitation of anti-quarks or anti-neutrinos would lead to a noticeably differently massed SN remnant). Of course we would like to be very sure with many more lines of evidence. :D
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[1] Modelling anti-matter anti-gravitation is not a popular academic area of enquiry, mostly because there's no evidence for it, and there's already lots of model-building in high-energy physics (and string-theoretical gravitation) where one has to "hide" side-effects that aren't seen around here-and-now somewhere in the universe (distant past or future, well outside the Hubble volume, or in extra dimensions) that solve a broader range of problems than introducing anti-matter anti-gravitation.
However, on that front, see Hossenfelder's blog entry http://backreaction.blogspot.com/2017/04/why-doesnt-anti-mat... which refers to her paper https://arxiv.org/abs/gr-qc/0508013 which does not deal with anti-matter as you conceive it in your question, because she proposes duplicating the ENTIRE Standard Model (including its anti-neutrinos, positrons, anti-quarks, etc.) that feels gravity normally with an exactly similar set of quantum fields that is feels gravity as a repulsive force. She then introduces an anti-gravitation which this second set of standard-model-like-fields feels as attractive, while the Standard Model is adapted so that its constituents feels it as repulsive. She likes toying with mathematics, and this is a classic example of building a model and chasing down its consequences just for fun -- she certainly does not propose that this is a plausible model of nature, since it breaks the equivalence principle in a way that conflicts with tests of it.
In her model for technical reasons the anti-gravitating extra set of particles have to be suppressed from Hawking radiation, and therefore are not evaporative of black holes. (They would be repelled from black holes if they were brought from outside a BH towards a BH, though, just as they would be repelled from the Earth if brought near the Earth). She does not elucidate a mechanism for this suppression.
Finally, Hossenfelder's model is single-metric, rather than the sketch of a bimetric approach that I described above. However, it's also closer to the exact wording -- if not the spirit -- of your comment.
> So tossing in antimatter would not do much. It would never cross the horizon in an external observer’s reference frame and thus would never interact with anything and thus would produce no effects.
It would never be directly seen crossing the horizon by the accelerated observers you are thinking about (it just gets redder and dimmer), but it sure crosses the horizon, and this can be seen by those observers indirectly: the mass term of the BH metric describing the exterior spacetime changes, with observables like the Einstein lensing subtending a greater angle and a change in the apparent location of the ISCO.
Consider the act of throwing a smaller black hole of mass M_small into a larger one of mass M_big: General Relativity tells us that within about a light-crossing time of the sum of the diameters of the two BHs there will be a larger BH of M_merged \lt (M_big + M_small) with the missing mass dumped into a large dynamical perturbation of your choice of background metric. (Linearizing this picture is literally how gravitational waves are studied; with the present detections of gravitational waves, we can be pretty confident that neutron stars do in fact cross into the horizons of black holes rather than gathering up as some structure microscopically close to the horizon, and even more clearly not as a long-lived bump near the horizon of a BH where J \gt 0).
There are of course other observers who could outright see the infallers cross the point of no return.
(Power-orbit yourself close to the horizon of an ultramassive black hole where the tidal forces at the horizon are even less than those we experience here on Earth. Poke your little finger through the horizon. By virtue of your orbit it will slice right off, and using a highly sensitive gravimeter you would detect it behind you as you continue on your orbit. If you don't believe in gravimeters that sensitive, feel free to substitute a prominent mountain on a rocky planet for your finger and you, and you could then use existing technology. (Also, you could use a highly elliptical orbit instead of a highly powered circular one) In either case, a distant outside accelerated observer has to contend with the redshift, and so won't directly see what happened, and might not be patient enough for you to communicate your results. Additionally, the "bump" will only survive for a fraction of your orbit around the BH, since the bump is hair that will be balded within about a light-crossing time. The ringdown will propagate as gravitational radiation which will get to distant outside accelerated observer sooner than you, or a message from you, will.)
In that situation wouldn't it be impossible to shove antimatter into a black hole in the first place because the gravity-antigravity force would repel instead of attract?
Long answer: When equal amounts of matter and antimatter collide, they are annihilated. They haven't disappeared or canceled out, they’re converted into pure energy. Both mass and energy are just different aspects of the same thing: you can turn mass into energy, and you can turn energy into mass. Black holes turn everything, both matter and energy, into more black hole.
Be careful, this is not correct and is a common misconception. You cannot turn mass into energy or energy into mass. This would violate not one, but two fundamental laws of physics - conservation of energy and conservation of mass.
A more appropriate way to think about this is simply that all energy has mass, and all mass has energy, and these amounts are related through the famous E=mc2.
Black holes destroy information don't they - they would be neither matter nor antimatter. Nor energy, for that matter. They're just point mass. Which implies that both matter and antimatter would be attracted to the black hole equally, but that kind of breaks the idea that antimatter reverse-curves spacetime, doesn't it?
So anti-black-holes would have to exist in a "antimatter has antigravity" universe, wouldn't it?
Which contradicts the idea of black holes destroying all information.
This is called the black hole information paradox. Today most physicists believe that hawking radiation preserves quantum information. Hawking himself made a bet that it doesn’t, but by 2004 he had become convinced and conceded the bet. But as far as I know this is still an open question - we’ve never detected hawking radiation experimentally.
That anti-gravity matter would need to be traveling faster than light to reach the black hole. It's the reverse problem of getting normal matter out of one.
But, it would mean that if you created a nuclear reactor inside a black hole, you would be able to communicate with the external world. That is problematic enough by itself.
