Spherically symmetric systems of fields and black holes. V. Predynamical properties of causal structure

We show that the constraints and the gauge-propagating equations alone are sufficient for apparent horizons to have the well-known classical properties: to be invisible from infinity and to have nontimelike world tubes. The proof is gauge invariant and the result holds for any gauge. Then, we derive, with the same assumption, some crucial features of the φ-orthogonal gauge, which has been used throughout this series of papers. The most important is that the corresponding foliation avoids apparent horizons. In this way, the constraints guarantee that the causal and asymptotic structure of the foliated part of the spacetime is the same for any kinematically possible trajectory of the field.