# Maximal globally hyperbolic developments of subluminal and superluminal quasilinear wave equations

# Maximal globally hyperbolic developments of subluminal and superluminal quasilinear wave equations

Please note the different time.A quasilinear wave equation in Minkowski spacetime is called subluminal (superluminal) if, in the tangent space, its characteristic cone lies inside (outside) the Minkowski null cone. Superluminal equations are widely believed by physicists to be “bad”: it is often asserted that such equations admit “causality violating” solutions exhibiting a Cauchy horizon beyond which one cannot predict what happens. To investigate this, I will consider an example of an equation which can be formulated in either a subluminal or superluminal version. I will show that the subluminal version exhibits the unusual property that there can exist multiple distinct maximal globally hyperbolic developments arising form the same initial data. The superluminal version does not exhibit this pathology. Therefore the superluminal equation exhibits better predictability than the subluminal one. I will present a theorem which explains why this behavior occurs, and under what circumstances there exists a unique maximal globally hyperbolic development. This talk is based on joint work with F. Eperon and J. Sbierski.