Abstract: Math Used in Studying Black Holes
Mathematics is essential in studying black holes, involved in every step from theoretical predictions to observations. In this talk, I highlight how mathematical principles enable us to predict, simulate, and image these extreme astrophysical objects. Using Einstein's equations of general relativity and differential geometry, we predicted black holes' properties. Simulating plasma dynamics around them involves numerically solving complex partial differential equations. Processing data from the Event Horizon Telescope—which captured the first images of black holes—requires advanced statistical methods. Reconstructing images from sparse and noisy data requires compressed sensing techniques. Our findings reveal strong magnetic fields and support high-spin models, demonstrating mathematics' crucial role in advancing our understanding of black holes.