Title: The Critical Collapse of a Perfect Fluid in Infinite Dimensions
Abstract: I will review a series of impressive numerical calculations from the 90s that revealed universal scaling behaviour in gravitational collapse. I will then focus on spherically symmetric perfect fluid collapse and explain how treating the number of spacetime dimensions, D, as an expansion parameter gives us analytic control of its continuously self-similar critical solution. In a 1/D expansion, we construct this solution and compute its critical exponent. At leading order, the length-scaling exponent is 1/2 and does not depend on the fluid’s equation of state parameter, a simplification reminiscent of mean-field behaviour. This rich system provides many potential routes for exploring universality in classical gravity. Based on a series of forthcoming papers with Guilherme L. Pimentel.