Red Matter: Trying to Explain Black Holes in Star Trek

Preface: I KNOW that Star Trek (2009) played merry hell with all sorts of physics. I'm not trying to explain how contrary they run to regular, ordinary physics; that's just too damn easy. What I'm going to try to do is explore their black hole physics, and see what the implications are when you bring them into line with the parts of black hole physics that they didn't explicitly rewrite. It's... oh, forget it. Just read on. Or don't. Whatever makes you happy.

The plot device J.J. Abrams came up with in the film is called "red matter", which is apparently different than any other matter that reflects red light.

This isn't a wayward red blood cell, it's black hole fuel!

The basic idea seems to be that when the red matter is released into something, it creates a black hole. But there are conditions under which it won't; you can keep it suspended in a tank, even poke it with a needle and take some of it out, and it's stable. It only turns into a black hole if you provoke it, much like your adorable cat, who will only turn into a hissing, spitting ball of painful death if you step on his tail. Otherwise, he will be calm, serene, and float peacefully in midair (as many cats do).

The trigger for red matter seems to be making it interact with a massive body, such as a ship or a planet. You can't just set a trigger on it and tell it to become a black hole, it has to actually hit the massive object. Moreover, I think it is best used at the spot in the object where matter is most compressed by its own gravity. Namely, the center. This is why Nero used his giant drill to bore down to the center of Vulcan, as opposed to just hurling the red matter at the planet's surface.

Here's where it gets interesting, though. The black hole that's produced has no correlation to the amount of red matter that's used. For example, observe this photo of the planet Vulcan collapsing into the black hole at its core.

Here it is again, a second later. You can see the last remnants of the planet at the center, and then the patch of darkness in the center of the frame that defines the Schwartzchild radius (effectively, the boundary of a black hole).

So the black hole that's produced, by a tiny drop of red matter, is approximately planet-sized. Compare that to the black hole produced when the entire huge case of red matter impacts Nero's ship:

The black hole formed in the middle of Nero's ship; that's why it's on both sides.

Sure, it looks big, but that ship is at best comparable to a big asteroid. Certainly not moon-sized, or planet-sized. The black hole produced from all that red matter was only about the size of the ship!

This leads me to believe that the amount of red matter is irrelevant. What matters is the thing the red matter is used on, and how much mass it has.

Now, this presents a bit of a problem. The black hole produced is not directly correlated to the amount of mass the object has.

Let's assume Vulcan, shown collapsing above, is about the size of Earth (for convenience's sake). If Earth collapsed into a black hole, the black hole produced would be smaller than a grape. A stellar-mass black hole--a black hole with the approximate mass of our sun--comes from the collapse of a star with 25+ solar masses. Yet the red matter made Vulcan collapse into a planet-mass black hole! Thus, red matter must work, not by collapsing the mass already present to its natural Schwartzchild radius (all masses have it; it's theoretical in nature, kinda), but by acting as a multiplier for the mass that's already there. It multiplies the mass of the object it's used on until the radius of the black hole that'll be produced is equal to the radius of the original object.

We can even work out what the multiplier is, within reason. Here's how I did it:

The Schwartzchild radius of an object (what it would be, with its mass, if it were to become a black hole) is about three kilometers multiplied by its mass. Now, the radius of the Vulcan black hole (if Vulcan is Earth-sized) is about 6384 kilometers, since that's the radius of Earth. Divided by 3, that means that you would have to have 2128 solar masses to create a black hole that size!

Earth's mass, obviously, isn't anything even close to a stellar mass. According to Wikipedia, it's about 332,950 times less than the sun. So if we multiply 332950 by 2128, we get 708,517,600. That's the multiplier of the "red matter", if my theory is correct. When the red matter hits a massive object (planet, ship, whatever), it multiplies the mass by 708,517,600 times, causing it to collapse into a  black hole that has a Schwartzchild radius precisely equal to the original object's actual radius.

This is how red matter works. Thank you and good night.

Here's some celebratory penguins!

(Obviously I've had to make some assumptions; Vulcan is supposed to have a stronger surface gravity than Earth, for example, so it's reasonable to assume that it's heavier. However, fuck it, I didn't exactly have precise numbers to work with. And whether the red matter number is the exact multiplier or not, the important thing is I've got a good idea of how the mechanism works and what the multiplier is within experimental error. That's a decent starting point.)