HN Theater @HNTheaterMonth

I don't know about those exact examples or how to compare them, because the subject doesn't really interest me enough to peruse the material when and if it is ever published, and unlike Bee I don't have a copy to read (or much motivation if I did).

The lack of interest hangs on the fact that we have highly-tested descriptions of our universe which have relativity baked right in. Even Alcubierre's "drive" paper [1] is written in the language of relativity. And thus we have to take seriously the problem that we have in relativity no obvious way to induce a warp bubble onto a patch of flat spacetime by scattering any configuration of known matter through that region.

We can create stars, including relativistic stars (neutron stars are an example) and black holes by depositing practically an infinite variety of matter into a region of flat spacetime. (In fact, if we use a solar mass of hydrogen gas then Raychaudhuri's focusing theorem makes it hard to avoid it coming together as a star eventually, and then probably a white dwarf).

Likewise, "large scale structure formation" is nearly inevitable with a handful of parameters which in the standard cosmology we capture and try to measure. There's lots of ways in an expanding universe to wind up with galaxies.

We can even get silly and contrive extremely unlikely initial configurations of known matter and simulate what happens. We can even simplify known matter by removing physical features that complicate the picture. This can even be useful. Historically one started with perfectly spherical arrangements of gas that does not self-interact (doesn't clump together, doesn't repel, doesn't induce twisting or spiralling) to try to understand the formation of spheroidal objects like stars, planets, and black holes. Then as tools to simulate such collapses became better and faster, adding back in the stripped-out physical aspects of real interacting matter (which clumps into molecules, and those in turn break apart as they get hot, etc., and probably never found in perfect spheres rather than discoids or blobs) for a better approximation of such systems.

No known matter has the properties necessary to create negative energy.

If we start with an extremely simple form of a purely classical non-interacting negative-energy-density non-relativistic dust that we can drop into the stress-energy tensor of the Einstein Field Equations, we can do some simulations and see what happens. [3] But we are complicating something wholly fictional. Nothing known has the requisite property (negative energy), and so there is no path to adding more complex behaviours to such a basic test set up to try to approach a physically plausible system.

Such an unknown substance is politely called "exotic matter" for the simple reason that it foreign to our solar system. "Unobtanium" is just as fair, if a little less polite.

And that, for me, leads to it being an uninteresting family of solutions.

In the very unlikely event we find some mechanism to generate any negative energy, then great, general interest will revive (and we'll start asking questions about what suppresses that negative energy such that it is undetected in our solar system and in various-sized systems (galaxy clusters, etc) we see in our sky).

Until then, I will tend to see such solutions to the Einstein Field Equations as starting with highly contrived metrics ab initio. I don't object to anyone investigating such things on strictly that basis: Schwarzschild's solution was highly contrived too, and was a matter-free eternal setup. But there were already pretty spherical gravitating systems around to examine (Schwarzschild lived on one!) and Newtonian methods to study those were useful for validating the Schwarzschild solution for objects wholly outside their own Schwarschild radius. But we should also think about the work of Kerr on axisymmetric rotating systems : it too was a contrived vacuum solution, but almost nobody (and certainly not Kerr himself [1]) thinks that we should think of the inside-the-horizons region as physical (and probably most relativists don't, for various reasons).

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[1] Alcubierre has left a copy at https://arxiv.org/abs/gr-qc/0009013v1 -- note the very first sentence of the abstract ("within the framework of relativity").

[2] "... negative mass instead of positive: that's NOTHING to do with physics." Around 28:05 at https://youtu.be/jji2pgfq7oE?t=1685 -- this lecture also shows that a very simple complication of an exact solution, just adding angular momentum to Schwarzschild -- is both very hard work and will often produce obvious garbage. Even Kerr's solution, as he himself says, is part garbage. Fortunately the garbage in Kerr's solution is hidden behind an event horizon, so we can decide not to care at all about that for systems that aren't dense enough to have event horizons, and can say that the inner parts of black holes are for all practical purposes purely a theoretical problem, since we know no way of investigating what goes on in there. Relatedly, Kerr at around that point in the video points out that we know how to arrange matter to form a rotating black hole with the features of the Kerr solution, and frankly, to me, since that is a true statement, that overrides any theoretical objections about the interior garbage. (We don't know how to arrange matter to form a warp bubble, and warp bubbles have nice quiet interiors and distant exteriors, but have tremendous garbage in the thin shell).

[3] Results tend to follow a pattern that we can think about using the idea of a gravitational charge. Unlike the electromagnetic charge, where like charges to repel, the gravitational charge causes like charges to attract. All known matter -- including dark matter -- has the same gravitational charge. So protons, neutrinos, photons, whatever the hell dark matter is, and so on all tend to collapse into structures like galaxies. "Negative" stuff has the opposite gravitational charge. Things with the opposite elecromagnetic charge tend to attract one another, but things with the opposite gravitational charge tend to repel one another. So if we brought a small amount of "negative" matter, with its opposite gravitational charge, into our solar system, it would be thrown out by all the normally-charged stuff (the sun, the earth, etc). Things get really absurd when one couples equally-massed equally-but-oppositely-gravitationally-charged matter together: you can create infinite power in some other charge (like the electromagnetic one) for instance. Again, this oppositely-gravitationally-charged negative stuff is called exotic because if there wasn't much of it in the early universe, it's all been thrown out of it since, and if there was much of it in the early universe, where the hell are all the side-effects ? (if we're talking about a tiny percent of negative stuff, a fraction of baryonic matter, then wormholes and warp bubbles should fill our sky almost as much as stars do, making all sorts of weird observables from gravitational lensing far from galaxies to odd emissions and absorption lines on light from distant quasars).