On one simple picture

Krisztián Pintér, 2019
pinterkr@gmail.com

This page is mostly for sci-fi writers, and newbie blackhole enthusiasts. Black holes come in many flavors, from the smallest, vigorous ones to the solar system spanning behemoths. They can be used as somewhat (very) cumbersome batteries, maybe weapons, or just a nice cozy living space to host quadrillions of people. On this page, we introduce a single image to showcase all of them.

Black holes are characterized only by their mass. Unlike stars that come in many different types, large and bright, or small and bright, black holes only have size, and everything else depends on it. Thus the map of black holes is a straight line. Every point on this line is associated with a certain size, luminosity, temperature, gravity, mass, radius and color. These all come in package. We could plot all black holes on a stripe, but we won't, because plotting them on a square looks cooler. So behold the engineering diagram of black holes below. And then some notes.

How to use

All types of black holes lie on the diagonal line. The line continues in both directions, this segment covers the meaningful range from subatomic unstable volatiles up to the largest monsters you can find in the universe. Pick any point on that line, and you can read off the properties on the axes. Of course you can start with any axis, and find the appropriate point on the diagonal that way. The digonal itself is also annotated, photon "color" on the right side, and equivalent temperature on the left. These tell the peak wavelength of the Hawking radiation.

Scale

Beware, not only all the axes are logarithmic, they are also "wide". Things appear close usually pretty far apart. For example you might think that a megaton sized black hole (10⁹kg) lives for a little over a year. But that approximation would be very loose, because it is more than 850 years. Which is, arguably, approximately a year considering the vast span of the axis, having unspeakable numbers on the right side.

Lifetime

When designing a black hole device, you pick a vertical band, between two time values. For example between 10⁹ and 10⁸, there is a 10⁹-10⁸=900 million seconds long period, during which the energy output will continue to grow from approximately 10¹⁵ watts to 10¹⁶ watts. You always want such a time window, because at the end of their lifecycle, black holes tend to become violent beyond measure. You either need to refeed them, or make sure you are far away when they go off.

Mass

Black holes are massive. They couldd be any light, but as you can see, anything below a ton will not have a considerable lifetime. Incidentally, a black hole as massive as a blue whale will live for a blink of an eye. It would also be smaller than a proton. Much smaller in fact. There is no real upper limit, but there are no processes in the known universe that could gather enough matter to create much larger black holes than the ones in the center of galaxies. They vary in size quite a bit, our own and the biggest known are included here.

Luminosity

Black holes lose mass through electromagnetic radiation. The smaller they are, the more they radiate. Reasonable sized black holes radiate extremely little, we would have hard time measuring it. Small ones on the other hand can be a little noise to say the least. This makes them a candidate for high power batteries, but this comes with numerous caveats. One being the unfortunate wavelengths they tend to emit. More on that later.

Radius

Black holes come in various sizes from subatomic to as large as entire solar systems. They are always very small compared to their mass. But since their mass is enormous, they can be pretty big still.

Wavelength

Black holes radiate at a typical wavelength similar to their size. If you look at the diagram, you see that black holes with high energy output (battery range) will be in the very hard gamma bands. You can build a huge X-ray device, if you don't mind its thousand gigaton weight. Visible or radio emitting black holes will be so low power, you will need sensitive equipment to detect the radiation, especially if they have an accretion disk, which will dominate the luminance. Many landmarks are actually ranges, but for simplicity only a typical value is shown. Most of them are self explanatory, but these might need explanation:

Temperature

This is the apparent temperature of the Hawking radiation. If the black hole was a black body (which it isn't really, even if called black), this is the temperature that would result in the same peak wavelength. Maybe the relationship is deeper, don't quote me on that.