What is inside a black hole is a mystery that we are still far from answering. Since nothing can come out of its interior, it is impossible for us to see what is inside, so our only way to investigate its interior is through theory. But sometimes when constructing these theories we can make a mistake when establishing the chain of mathematical or logical propositions on which the theories are based.

And that is something that could have even happened to Stephen Hawking himself.

The replica. This is how he defends it a job published on platforms ArXiv and Researchgate. The article might have perhaps gone unnoticed if it were not for having been signed by a heavyweight in cosmology, Roy Kerr. The article calls into question nothing less than the notion that within black holes singularities exist. He does so by falsifying one of the mathematical arguments from which Roger Penrose and Stephen Hawking built their theorem on singularity.

But what is singularity? And who is Kerr? We can answer both more or less at the same time.

At the origin. The idea of ​​the existence of black holes comes from Einstein’s relativity and the so-called Einstein field equations. From these equations, the German physicist Karl Schwarzschild conceived what we could consider the simplest theoretical model of a black hole.

In this model two parts can be distinguished: an event horizon that delimits the volume of space where the gravitational influence of the black hole is so great that not even light can escape; and a singularity, a point in space and time where the density is such that their curvature becomes infinite.

Solving problems. There was a problem, and that is that all celestial bodies, at least partly due to gravitational interactions, tend to rotate. Solving Einstein’s field equations statically was one thing, but if angular momentum was to be taken into account… things became more complicated. So much so that it took almost half a century until a black hole model that took this rotation into account. The person who solved this problem was Kerr himself. The year was 1963.

Although the so-called Kerr black holes have singularities (one in the shape of a ring instead of being concentrated in one point), this mathematician The 91-year-old has labeled as “faith, not science” the current consensus around the idea that black holes have singularities in their respective interiors.

The counterargument. He does so by questioning one of the arguments that Penrose and Hawking once proposed when defending the existence of singularities. The argument starts from the affine length of light. Light does not “age” since everything that moves at speeds close to that of light, but the affine length allowed theorists to have an analogous measurement of its “life cycle.” As we saw recentlyKerr’s theory is not without problems and has also been disputed.

A singularity? Starting from the fact that this affine length was finite, Penrose and Hawking concluded that the point at which the light “ended” could not be anything other than a singularity. This is an argument that has remained in force for more than half a century and which Kerr has attacked in his latest work, proving, also mathematically, that this finite affine length did not necessarily have to imply the existence of a singularity.

If Kerr is rightPenrose and Hawking would have screwed up their argument in favor of the existence of singularities, but does that mean that singularities do not exist? Well no, neither. Refuting a proof is one thing and refuting a hypothesis is quite another. As I pointed out the physicist and popularizer Sabine Hossenfelder, a test can be erroneous without the conclusion ceasing to be correct.

many doubts. There may be different ways to construct this hypothesis, and this is the case of singularities. We can start by remembering that is the theory of relativity In itself, what invites us to think that singularities exist inside black holes; the affine length is just one way to demonstrate this mathematically. As Hossenfelder explains, we do not know the force or reason why matter can be compressed enough as a cause of gravitational attraction to end up fulfilling Einstein’s prediction.

We still don’t know much. The last issue to keep in mind that German physics reminds us of has to do with the fact that there is still a lot we don’t know about physics. What we think we know about black holes is based on relativity and what we know about gravity, but this theory has not yet been proven. sharing with what we know about quantum, particle physics and fundamental interactions in a “theory of everything.”

For many physicists, quantum effects can make the interior of black holes be very different from what we conceive today. And they could even, hypothetically, be that force that prevents the emergence of the singularity. Perhaps this unified theory is our only safe passage into a black hole. Theoretically, of course.

In techopiniones | This exciting discovery puts in our hands the possibility of understanding the life of stars much better.

In techopiniones | The Webb telescope has observed quasars where they shouldn’t be. Something is wrong with the theory of black holes

Image | NASA/JPL-Caltech

*An earlier version of this article was published in December 2023