An international group of scientists finally proved that slowly rotating Kerr black holes are stable, a report from *Quanta Magazine* reveals.

In 1963, mathematician Roy Kerr found a solution to Einstein’s equations that accurately described the spacetime around what is now known as a rotating black hole.

For decades, scientists have tried to show that these types of black holes are stable. They have finally devised a solution that proves the stability of the slowly rotating variety of Kerr black holes. To do so, they built on years of work related to Kerr's models.

## Stable rotating black holes

If a black hole is stable, it will eventually revert to Kerr's mathematical description, even after receiving an intense jolt from gravitational waves. If these black holes were unstable, it would mean Einstein's theory of gravitation would have to be modified at a fundamental level, and the scientific community would have to reassess what it knows about the cosmic giants.

The scientists behind the new formula considered whether gravitational waves hitting a black hole could cause enough disruption to alter or even destroy a black hole permanently. As a point of comparison, a wine glass will start to vibrate and can even shatter if it's met with enough sound waves that perfectly match its resonant frequency.

They considered several outcomes, such as a gravitational wave crossing the event horizon of a Kerr black hole to enter its interior. This could alter the black hole's mass and rotation. They posited that gravitational waves could also congregate and spin with such energy around the black hole that they create an entirely new singularity—a sure sign of instability.

## 'A triumph for the whole field'

The scientists are made up of three mathematicians: Jérémie Szeftel from Sorbonne University, Elena Giorgi of Columbia University, and Sergiu Klainerman of Princeton University. They built on the work of others in the field to finally prove that Kerr black holes are stable. "There have been four serious attempts,” Klainerman said, “and we happen to be the lucky ones.” It is “a triumph for the whole field.”

The three mathematicians proved stability for slowly rotating black holes, which has not yet been demonstrated for rapidly rotating black holes. Their work is also yet to be peer-reviewed, though previous related work by the same scientists has been approved for publication.

The new result constitutes "a milestone in the mathematical development of general relativity,” Demetrios Christodoulou, a mathematician at the Swiss Federal Institute of Technology Zurich, told Quanta Magazine. These new mathematical models, alongside new imaging technology from the Event Horizon Telescope, mean we have a greater understanding of the colossal black holes at the center of many of the universe's galaxies.

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