# Drawing Blanks

Premature Optimization is a Prerequisite for Success

I’m still up at 1am because someone on the Internet is wrong. Someone has posted on Reddit a short sci-fi essay about black holes, and many people have taken it for an accurate description: http://www.reddit.com/r/askscience/comments/f1lgu/what_would_happen_if_the_event_horizons_of_two/c1cuiyw?context=2

I am not going to address every statement in that post. Anyone who has seen space-time diagrams and causal diagrams of black holes will be able to see the most striking inaccuracies. I’ll just say a few words about horizons and singularities which may help to clear some things out.

First of all, nothing special happens as you cross the event horizon. There is no discontinuity in your observations. Moreover, it is fundamentally impossible for you to determine the event when/where you cross it.

So is it true that you’re doomed once you’ve crossed the horizon? Yes. But if you stay away from black holes you are still doomed. All world lines end sooner or later (or maybe infinitely later) at the End of the Universe. The question is, how many ticks of your clock it will take. Take the photons for example. Poor things are already dead the same instance they are born, by their clock.

The black hole singularity is another kind of the End of the Universe. It can be reached sooner rather than later not just by the photons, but also by subluminal travelers. For a nearby observer, the singularity is not a point in space. It is a moment in time. So when is it? It is precisely at the End of the Universe.

So what is the event horizon? It is a surface in space-time that separates the events that are doomed to reach the singularity from all other events. What shape is the horizon? It is not useful to think of it as a surface in space. It is shaped exactly as a light cone: a null (light-like) surface in Minkowski space. So are you really “surrounded by the singularity” once you fall through the horizon? Only in the same sense as you now are “surrounded by tomorrow”. And of course the singularity will not prevent you from seeing the light from the stars. The fact that you are doomed to enter the tomorrow’s day doesn’t prevent you from meeting other doomed people today.

Is there at least anything Lovecraftian about the black hole? Well, on the causal diagram the singularity looks as if someone bit off the time-like infinity to bring the End of the Universe closer to us. But that doesn’t look like Cthulhu’s bite. Looks more like Stephen King’s Langoliers to me.

That’s about it with regards to the causal issues. If you are not familiar with causal diagrams, please do yourself a favor: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/black_holes_picture/index.html

A few words on the gravitational issues. What about the light orbit, isn’t that a distinctive feature of the horizon? No, the light cannot orbit the blackhole at the horizon. It can orbit the blackhole at 1.5 Schwarzschild radii. Below that distance there are no closed orbits. What about the “infinite tidal forces that tear apart the fabric of space itself”? Isn’t that a distinctive feature of the horizon? No. Supermassive blackholes may have very small tidal forces at the horizon.

If you want an accurate picture of what happens as you fall through the horizon, read this: http://casa.colorado.edu/~ajsh/singularity.html