Predictability of Subluminal and Superluminal Wave Equations

Abstract: It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations. To investigate this, we study the Born–Infeld scalar in two spacetime dimensions. This equation can be formulated in either a subluminal or a superluminal form. Surprisingly, we find that the subluminal theory is less predictive than the superluminal theory in the following sense. For the subluminal theory, there can exist multiple maximal globally hyperbolic developments arising from the same initial data. This problem does not arise in the superluminal theory, for which there is 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. In particular, we prove that superluminal equations always admit a unique maximal globally hyperbolic development. In this sense, superluminal equations exhibit better predictability than generic subluminal equations

Strong cosmic censorship in de Sitter space

Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analysis covers both scalar field and linearized gravitational perturbations

Plausible scenario for a generic violation of the weak cosmic censorship conjecture in asymptotically flat four dimensions

We present a plausible counterexample to the weak cosmic censorship conjecture in the fourdimensional Einstein-Scalar theory with asymptotically flat boundary conditions. Our setup stems from the analysis of the massive Klein-Gordon equation on a fixed Kerr black hole background. In particular, we construct the quasinormal spectrum numerically, and analytically in the WKB approximation, then go on to compute its backreaction on the Kerr geometry. In the regime of parameters where the analytic and numerical techniques overlap we find perfect agreement. We give strong evidence for the existence of a nonlinear instability at late times