On February 25th we presented our project at the regional Jugend forscht competition. Our topic was theoretical physics, which is already unusual in a competition where many projects are experimental or technical. We worked on a question related to black holes and Einstein’s theory of gravity. The project is called The Kerr Trisector Closure.
General Relativity describes gravity as the geometry of spacetime. According to the theory, mass and energy curve spacetime, and that curvature determines how objects move, how light propagates, and how gravitational waves are emitted. Over the past century, the theory has been tested many times. We have confirmed the motion of planets, detected gravitational waves from merging black holes, and even taken images of black hole shadows. However, most of these tests examine one physical effect at a time. Orbital motion is tested separately. Ringdown oscillations are tested separately. Black hole imaging is analyzed separately. Each test checks whether General Relativity works in that specific regime. But there is a deeper question that is not often addressed directly. If all these effects are governed by the same spacetime geometry, then independent measurements of the same black hole should agree on the same parameters.
A rotating black hole in General Relativity is described by the Kerr solution. This solution depends only on two physical parameters: the mass $M$ and the dimensionless spin $\chi$. Once these two numbers are fixed, the entire external spacetime geometry is determined. Orbital motion, gravitational wave frequencies, and the bending of light are all controlled by the same pair of values. This idea led us to a simple but powerful hypothesis. If General Relativity is correct, then independent measurements of mass and spin from different observational sectors should be statistically consistent with one single Kerr spacetime.
To test this, we considered three physically independent ways of measuring a black hole. The first sector is orbital motion. When two compact objects spiral into each other, they emit gravitational waves. The shape and frequency evolution of these waves allow us to estimate the mass and spin. This gives one parameter pair, which we denote as $M_{dyn}, \chi_{dyn}$.
The second sector is the ringdown phase. After a merger, the newly formed black hole oscillates and settles down. The frequencies and damping times of these oscillations depend only on mass and spin. From this we obtain another estimate, $M_{rd}, \chi_{rd}$.
The third sector is black hole imaging. Light near a black hole follows curved paths due to strong spacetime curvature. This produces a shadow and photon ring structure. The size and shape of this shadow depend on mass and spin, giving a third estimate, $M_{img}, \chi_{img}$.
If General Relativity is correct and the Kerr solution describes reality, these three measurements should agree within their uncertainties. We then developed a mathematical framework to test this consistency. Each sector provides a parameter estimate with an associated uncertainty. We combine the three measurements and compute a common best fit spacetime. After that, we calculate a quantity called the closure statistic, denoted by $T^2$. This value measures how far the three sector estimates deviate from the common solution, taking their uncertainties into account.
If $T^2$ is small, the measurements are statistically consistent and the spacetime is closed. If $T^2$ is large, at least one sector disagrees with the others beyond what measurement errors can explain. In the case of three sectors and two parameters, the statistic follows a chi squared distribution with four degrees of freedom if everything is consistent. This gives us a precise rejection threshold. If the observed value exceeds this threshold, we reject the hypothesis that one single Kerr spacetime explains all three sectors. But since no single astrophysical black hole has yet been measured with high precision in all three sectors simultaneously, we tested our method using simulated data. We generated artificial measurements with realistic uncertainties and verified that the closure statistic behaves exactly as predicted. When the simulated data were consistent, the method did not produce false alarms. When we introduced a controlled inconsistency in one sector, the method detected it reliably.
An important feature of the Kerr Trisector Closure is that it can also identify which sector causes the inconsistency. By decomposing the total statistic into sector contributions, we can see whether the deviation comes from orbital dynamics, ringdown physics, or light propagation. This makes the framework not only a consistency test but also a diagnostic tool.
Our presentation at Jugend Forscht
Presenting this at Jugend forscht was intense. The topic is abstract and mathematical, and explaining it clearly in a limited time was challenging. But the core idea is simple: if gravity is geometry, then different ways of observing that geometry must agree. Winning 1st place was an incredible moment for us. It showed that even a purely theoretical project can compete at a high level when the idea is clear, logically structured, and carefully developed. This project is only a first step. Future gravitational wave detectors and improved black hole imaging experiments may eventually allow the Kerr Trisector Closure to be applied to real data. If that happens, we will have a new way to test whether Einstein’s description of spacetime remains self consistent across multiple physical regimes.