As mentioned in our previous updates, we are thrilled to announce that tomorrow marks the grand unveiling of our Kerr Trisector Closure. After months of dedicated development and meticulous writing, we are filled with satisfaction and readiness to embark on the next phase of our project.
The Kerr Trisector Closure
The Kerr Trisector Closure is about testing General Relativity in a deeper way than usual. Einstein’s theory says that gravity is not a force, but the bending of spacetime. A rotating black hole, according to General Relativity, is completely described by just two numbers: its mass (M) and its spin (a). These two parameters determine everything about the black hole. How objects orbit around it, how it vibrates after a merger, and how light bends near it. If the theory is correct, all observable effects around that black hole must come from the same spacetime geometry defined by those two numbers.
So far, scientists have tested General Relativity in many ways. They have studied the motion of objects spiraling into black holes (inspiral), the vibrations of black holes after collisions (ringdown), and the images of black hole shadows taken by telescopes like the Event Horizon Telescope. Each of these tests agrees with General Relativity on its own. However, they are usually analyzed separately. No one directly checks whether all three methods give the exact same mass and spin for the same black hole at the same time.
The Kerr Trisector Closure changes this. It compares three independent measurements of the same black hole: one from orbital motion, one from gravitational-wave ringdown, and one from imaging. Each method gives its own estimate of mass and spin, along with some measurement uncertainty. If General Relativity is fully correct, these three estimates should agree within those uncertainties. In other words, they should “close” to a single consistent spacetime description.
To test this, the method defines a statistical quantity called the closure statistic, $T^2$. This number measures how far apart the three measurements are, while properly accounting for their uncertainties. If $T^2$ is small, the differences between the measurements can be explained by normal experimental error, and the spacetime is considered consistent. If $T^2$ is too large, the differences are bigger than what uncertainty can explain, meaning at least one sector does not match the others. In that case, the assumption that a single Kerr spacetime describes everything would fail.
In simple terms, the Kerr Trisector Closure asks a powerful question: does one single spacetime geometry explain motion, vibration, and light around a black hole at the same time? If the answer is yes, General Relativity passes a very strict self-consistency test. If the answer is no, it would show exactly where the theory begins to break down.
Our final project files:
handout.pdf (handouts for summary)
project_jufo_26_de-3.pdf (simplified for the juries)
The_Kerr_Trisector_Closure (actual paper)