(The Herald Post) – Black holes have long captivated scientists and the general public alike with their mysterious nature and almost unfathomable power. As astrophysicists detect X-rays emitted when black holes feed, analyze gravitational waves from black hole collisions, and even image these cosmic behemoths, mathematicians like Elena Giorgi of Columbia University are taking a different approach: delving deep into the mathematics of general relativity to unravel the secrets of black holes.
According to Giorgi, “Black holes are mathematical solutions to the Einstein equation,” which is the “master equation” that underpins the general theory of relativity. Together with her colleagues, Giorgi works to prove theorems about these solutions and scrutinizes the mathematics of general relativity in hopes of unlocking previously unknown truths about black holes or corroborating existing hypotheses.
Christoph Kehle, a mathematician at ETH Zurich’s Institute for Theoretical Studies, explains that by focusing on general relativity, mathematicians can comprehend clear mathematical statements and study them, providing unambiguous answers within the framework of the theory. This enables them to tackle equations that address questions about the formation, evolution, and stability of black holes.
In a breakthrough paper published last year, Giorgi and her team resolved a long-standing mathematical question about black hole stability. They demonstrated that a stable black hole, in mathematical terms, is one that returns to a state similar to its former self after being disturbed, much like a stretched rubber band that snaps back upon release. This result is crucial, as it confirms that the math describing black holes accurately reflects their presumed stability.
Mathematics has a rich history of contributing to our understanding of black holes. Karl Schwarzschild’s 1916 solution to Einstein’s equations provided early insights into the nature of black holes, while Roger Penrose’s 1965 paper described how matter could collapse to form a black hole with a singularity at its core, earning him the 2020 Nobel Prize in Physics. Additionally, Roy Kerr’s 1963 discovery of a solution for rotating black holes was a game-changer, as it helped establish the existence of black holes in the real world.
Using a “proof by contradiction” method, Giorgi and her colleagues demonstrated that slowly rotating Kerr black holes are mathematically stable. Their nearly 1,000-page paper is currently under peer review. However, the result does not yet extend to quickly rotating Kerr black holes, which are also known to exist in the universe.
Giorgi’s research on black holes with an electric charge has led her to a new mathematical definition of electromagnetic radiation, which could be applied to further studies on charged black holes. As she continues to straddle the fields of physics and mathematics, Giorgi’s work is a testament to the power of interdisciplinary research in expanding our knowledge of the universe and its most enigmatic phenomena.