What's so scandalous about a naked singularity?

The centers of black holes are among the strangest places in the universe — so strange that current physics can't even describe them. Could these singularities be found out in the open? In this week's "Ask a Physicist" we find out.

Illustration by Markus Gann/Shutterstock

Let's face it: black holes are awesome, which is probably why I get so many questions about them. We've already talked about how they warp space and time (and how that would kill you), how they will ultimately evaporate and how they almost certainly don't make up the missing dark matter.

Today we're going to talk about what life is like at the very centers of black holes — the singularity — and whether we'll ever get to see any "naked singularities" out there in the cosmos. This week's question comes to us from Scott Rehm who asks:

The idea of a naked singularity seems bizarre to me. If the event horizon truly is just the "line of no return" and is simply there because of the very nature of singularities, how can you have a singularity without one?

I've talked a fair amount about black holes in in previous columns and, of course, in my book. As io9 readers, you were almost certainly familiar with the basics before I came along: A black hole is a region of such strong gravitational pull that nothing can escape not even light.

The point of no return, as you know, is referred to as the "Event Horizon" which is what Scott was talking about. To give you some idea of the scales involved, for a black hole the mass of the sun, the event horizon is at a radius of about 3 kilometers, and if you could somehow smash the earth down to a black hole, it would only have a radius of about 9 mm. (Note to belligerent super-intelligent aliens: Please don't.)

The takeaway from my article on falling into a black hole is that from your perspective as you fall in, crossing the event horizon pretty quickly, and for stellar mass black holes, you get killed very quickly — it takes about a tenth of a second between mild discomfort and being ripped to shreds by tidal forces. To someone far away, all of this seems to take literally forever.

Why are singularities a big deal?

Supposing you make it past the event horizon alive, and the physics becomes even crazier. For one thing, you no longer have any real freedom of motion. Not only can't you escape the event horizon, but you can't move outward at all. There's just an inexorable inward fall. But the biggest surprises await you at the very center of the black hole.

And what happens at the center? There's a singularity (No, futurists. Not that kind). The singularity is a point of literally infinite density where the physics gets incredibly wonky, and not just because there are infinities flying around.

Relativity and Quantum Mechanics are the two great physical theories of the 20th century. The former is supposed to describe gravity in general, and it does an exceptionally good job in strong gravitational fields, like the kinds found in and around black holes. Quantum mechanics, on the other hand, is supposed to describe the world of the very small, electrons, atomic nuclei and such. You'll probably remember it best as giving rise to uncertainty and collapsing wavefunctions.

Singularities have both incredibly strong — infinitely strong, really — gravitational fields and are infinitely small, and under those circumstances, relativity and quantum mechanics predict very different things. Let's make this clear: while you'll read a fair amount of speculation in the popular press, we do not currently have a working theory of quantum gravity and that means that we don't really know what happens at the centers of black holes. Put another way, if we really did understand what happens in singularities, we'd be a hell of a lot closer to unifying all of physics.

In case you think that singularities are only the province of black holes, I should point out that understanding singularities also means understanding the very beginning of time. The big bang itself was also a singularity — an instant of literally infinite density — and we don't have a handle on that either. Instead, cosmologists tend to start the clock around 10^-43 seconds after the big bang when relativity and quantum mechanics were different enough from each other for us to say anything useful at all.

What's so scandalous about a naked singularity?

Naked Singularities 101

Since light can't escape the black hole, the singularity is (and please imagine me using my spooky voice and flailing my fingers around for this next part) shrouded in mystery. Any signals coming from singularities inside a black hole necessarily travel at the speed of light or slower, and so will be trapped within the event horizon. Truth to be told, we don't get to see black holes directly, but that's another column. Even if you wanted to study them close up (and managed not to die in the process) the event horizon would stop you from transmitting your findings to the rest of the universe. You would have foolishly given your life for science in vain.

What if you wanted to study quantum gravity without all of the dying. Is there a chance that there are any singularities without event horizons, so-called "naked singularities" (which, like many things in Physics, including "contact friction", and "big bang" and physicists themselves, is less sexy than it might first appear) out there in the universe?

Maybe.

Most of the time when some physicist (including me) talks about black holes, they're talking about the most boring kind possible, the so-called "Schwarzschild" solution. These guys are unchanging, unspinning, and uncharged electrically and real black holes may be none of those things. We describe these idealized solutions because they are relatively simple to write down, easy to describe, and are a pretty good approximation to most real black holes.

More complicated objects, including spinning black holes, don't have just a simple event horizon. The details are a little complicated, so I'm going to give you a cartoon version. I know that there are a few experts who read this column, so as a heads-up to you folks, this is just meant to be an analogy. Imagine taking the world and spinning it really, really fast. If you spun it fast enough, people would fly outward from the surface, just like the gravitron at an amusement park. In other words, you can partially cancel gravity.

With enough math, you can crank through the mass of a rotating "Kerr" black hole, and the effects are similar. The faster it spins, the smaller the event horizon. Since it turns out, though, that practically speaking you can't spin it fast enough to make the event horizon disappear entirely, which means you can't make a naked singularity just by spinning a black hole fast enough. This problem is pretty typical. Researchers have been looking for solutions that include naked singularities for more than 60 years and haven't found them yet.

Can Naked Singularities exist?

These objects are so strange, so abhorrent, and so reclusive view that in 1969, Roger Penrose proposed the Conjecture of Cosmic Censorship:

No imploding object can ever form a naked singularity; if a singularity is formed, it must be clothed in a horizon so that we in the external Universe cannot see it.

Aficionados of pop-sci might note more than a whiff of similarity between this and Stephen Hawking's famous "Chronology Protection Conjecture" that I discussed in my column on time travel. Both are essentially statements on how people think the universe should work (informed by the fact that we haven't yet seen either working time machines or naked singularities — or versions of either that are fully consistent with the physics we know to be true), rather than what we can currently prove.

Hawking took a very dim view of naked singularities and in 1991 he bet Kip Thorne and John Preskill that naked singularities would never be discovered, mathematically or otherwise. As it happens, Hawking almost immediately found a possible loophole to produce something like naked singularities as a remnant of a black hole once it evaporates using, you guessed it, Hawking radiation. Still, this was just a guess, and was outside the formal terms of the bet at any rate.

Short of actually discovering a naked singularity out there in space, the next best approach is to make some sort of educated guess and run all of the numbers through a computer, since the calculations are clearly beyond the scope of puny humans. In 1997, Matthew Choptuik, then at UT Austin, did just that, and ran a simulation which involved a very precise configuration of a rotating, collapsing black hole — and it produced a naked singularity.

Computer simulations not good enough for you? What kind of nerd are you?

Well, they were almost good enough for Hawking, who grudgingly conceded that naked singularities could exist. The terms of the bet required him to provide Thorne and Preskill articles of clothing (because the bet was all about nakedness. Get it?) with a contrite message admitting he lost. He gave them the shirts, but the message wasn't so contrite. It read, in a fairly antagonistic way,"Nature abhors a naked singularity."

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (follow us on twitter, facebook, twitter or our blog.) He is an Associate Professor of Physics at Drexel University and is currently working on a new book on symmetry. Feel free to send email to askaphysicist@io9.com with any questions about the universe.