Black Hole Singularites "Faith, not science!" Prominent Physicist Claims

[This is a transcript with links to references.]

This is the maybe most surprising development in theoretical physics I’ve seen for a decade or so. A well-renown physicist is saying that there’s a mistake in a proof that dates back half a century, and black holes might not actually contain singularities.

The physicist in person is Roy Kerr, who is famous for his contributions to General Relativity. He was the first to understand how to mathematically describe rotating black holes in Einstein’s theory. Prior to this, physicists only know how to describe black holes that sit still. But in reality, when you have matter that undergoes gravitational collapse, it will generically have some angular momentum. And that angular momentum is conserved, so the final black hole must be spinning. If you want to describe real black holes, therefore, you need the maths to describe their rotation. And that’s what Kerr managed to do. These rotating black holes are therefore also known as Kerr black holes.

Black holes are characterized by their horizon, which is the surface of a region that you can only get in, but not out. I just explained in a recent episode on time-travel that Kerr black holes are incredibly weird because they have two horizons, and it seems that between them you can actually go back in time. Whether that is really possible or not, no one knows, but it shows that we don’t really understand these solutions.

Besides the horizon, black holes all have singularities inside, or so we thought. The singularity is a place where the curvature of space-time becomes technically infinitely large. With this, tidal forces become infinitely large, so everything will be ripped apart as it approaches the singularity. The horizon itself does not have a singularity.

Now, in the early days of general relativity, some physicists said that black holes are mathematical artifacts, they cannot exist in reality. Then Stephen Hawking and Roger Penrose said, no, it’s the other way round: When matter collapses, it’s impossible to prevent black holes from forming, and they all must have a singularity inside. These are the famous Hawking-Penrose singularity theorems. They should have both won a Nobel prize for it, unfortunately Hawking died before that. Penrose got the Nobel Prize in 2020.

Kerr now says there’s a mistake in that proof. His argument is roughly the following. Hawking and Penrose used an argument about the length of curves. They basically said in a black hole spacetime there are curves which have finite length  and the only way this can happen is if there’s a point where they end, which is a singularity.

The problem is that the length of a curve is usually related to the time that passes on the curve, which is called the proper time. But for light, no time passes, so for the curves on which light moves you need to measure the length in some other way. You do this by what’s called an \æfain\ parameter. If you don’t know exactly what this is, don’t worry, relevant is just that the affine parameter isn’t the same as time, so why worry if it ends?

Kerr now says that the Hawking-Penrose proof draws wrong conclusions from this affine parameter. If the affine parameter ends, that doesn’t mean that the curves end at any finite time because those are to different things. In the example he gives, the affine parameter is an exponential function of time. Then it will be bounded from below, so it kinda ends, but the curve still continues for all times, so no singularity.

In his paper, Kerr doesn’t mince words. He writes “Why do so many believe that the star inside must become singular at this moment? Faith, not science! Sixty years without a proof, but they believe!”

It seems to me that Kerr’s argument is almost certainly mathematically correct. And it’s, to the shame of many theoretical physicists, including myself, not even a particularly difficult argument. The question is then what this physically means. There are three things that came to my mind immediately.

First, just because the proof that black holes contain singularities isn’t correct doesn’t mean that the conclusion isn’t correct. It might be that this distinction which Kerr pointed out actually tells us something about the type of singularity rather than about whether they’re present or absent, and someone else will complete the proof.

The second thing to know is that there are other reasons physicists think black holes give rise to singularities which are more on the physical side. Most importantly it’s that if you compress matter beyond a certain critical density, we don’t know any force that could create enough pressure to stop it from completely collapsing. And we have numerical simulations for that, though those of course never really create singularities because that’d blow up even the best computer.

The third thing to know is that most physicists don’t think there’s a singularity inside black holes in any case. It’s because near the singularity they expect the quantum effects of space-time to become important, but we don’t have a theory for that. Though maybe now we do, if you remember yesterday’s episode. What’s new about Kerr’s argument is that he says you don’t need those quantum space-time effects to get rid of singularities.

Little Albert is mightily impressed by this paper and also slightly amused that so many physicists could have been so wrong for so long.