T1 - Predictability of Subluminal and Superluminal Wave Equations In this sense, superluminal equations exhibit better predictability than generic subluminal equations. In particular, we prove that superluminal equations always admit a unique maximal globally hyperbolic development. For a general quasilinear wave equation, we prove theorems establishing why this lack of uniqueness occurs, and identify conditions on the equation that ensure uniqueness. This problem does not arise in the superluminal theory, for which there is a unique maximal globally hyperbolic development. For the subluminal theory, there can exist multiple maximal globally hyperbolic developments arising from the same initial data. Surprisingly, we find that the subluminal theory is less predictive than the superluminal theory in the following sense. This equation can be formulated in either a subluminal or a superluminal form. To investigate this, we study the Born-Infeld scalar in two spacetime dimensions. In this sense, superluminal equations exhibit better predictability than generic subluminal equations.Ībstract = "It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations. It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations.
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