The Maddening Simplicity of Black Holes

Black holes.

The name is said to come from the Black Hole of Calcutta, an infamous prison that you cannot escape from. It is a fitting name, for black holes are the ultimate cosmological prison.

Black holes are defined by their event horizon, which is an imaginary line drawn through space and time. There are no warning bells, no klaxons, no sign or signal or evidence of its existence. But it’s there. And crossing it means simply this: you can never turn around. If you compress matter into a small enough volume you create an event horizon. You can enter this region of space, but you cannot leave. You are simply cut off from the wider universe, never to be seen or spoken to again.

This impossibility of return applies to all things in the universe, up to and including light itself. And so even though these event horizons exist as mathematical curiosities, they have a physical manifestation: they appear completely, utterly, totally blank.

Black holes exist as their own separate domains in the universe, their internal affairs forever hidden from view, the shades of the event horizon forever drawn against our curious gaze. That is one of many reasons that black holes are perhaps the most frustrating entities to inhabit the cosmos. The frustration comes from the fact that they seem to have two disparate natures: on the one hand, they are bizarrely simple creatures. But on the other, they completely defy our ability to explain them with our current understanding of physics. And it is in that dual nature where we just might find the knife that opens the next revolution.

Black holes were discovered in the mathematics of Einstein’s general theory of relativity, and those same mathematics tell us that black holes are, to the delight of every graduate student forced to learn about them, refreshingly simple.

If I wanted to develop a mathematical model to describe you, that model would need to require an incredible list of raw numbers. My model would have to take into account every physical proportion of the human body, every potential feature of skin and hair and sweat, every possibility of mood and temperament and intelligence. Capturing the totality of you would be a formidable task, requiring an almost endless number of equations, each one containing a variety of adjustable parameters to fully encapsulate the fact that you are different than anybody else.

Amazingly, black holes are simpler than people. We have our equations, as told to us by Einstein and Schwarzschild and the rest, that instruct us as to the nature of spacetime within and around them. Those equations tell us about event horizons. They tell us what happens to hapless wanderers who stray too close. They tell us about the gravity we experience near them.

And to tell one black hole apart from another, those equations have as free parameters only three numbers. Three numbers! That’s all it takes to completely describe everything you ever need to know about a black hole. Mass, electric charge, and spin. That’s it. If you encounter a black hole in the wild and measure those three properties, you have all you need. Your work is done. General relativity will tell you the rest.

This means that black holes aren’t just hiders of light, they are hiders of knowledge. Of information. They forget, or at least lock away forever, the secrets of what forged them and what fell below the event horizons later. You can fashion two black holes, one by cramming interstellar dust clouds into a small enough volume, and the other by cramming all your worst enemies into a small enough volume. These two black holes couldn’t be made of more different material, more different information – the information content of gas cloud, a recording of the positions and velocities and interactions and potentials of every subatomic particle, is wildly different than the same accounting of a human being. But if these two black holes end up with the same exact mass, electric charge, and spin rate, then they will be identical.

This is the so-called “no hair theorem”, a term coined half as a joke (and reviled by Richard Feynman) that has nevertheless stood the test of time. Black holes have no extra information on them, just as a bald head has no extra information on top of it. You can build a black hole however you want, out of whatever material you wish, taking as long or as short in the process as you please, and the black hole will consume all that information, all those records of what was and what could have been, and wrap an event horizon around it all, leaving us on the outside with three simple and mute numbers to describe it.