Propagation and horizon formation in Einstein--Gauss--Bonnet scalar collapse. I. Characteristic conditions, bounds and formation

Abstract

We study scalar collapse in five- and six-dimensional Einstein--Gauss--Bonnet gravity with positive coupling, treated as an exact classical theory. On spherical scalar backgrounds, the characteristic conditions of the tensor, vector and scalar gravitational sectors reduce to inequalities in two local invariants: $K=1+\tildeαF/R^2$, which compares the enclosed mass with the areal radius $R$, and a scalar-gradient invariant $j$. In five dimensions they imply $R_h^2>\tildeα$ for the areal radius $R_h$ of a regular marginal sphere on the GR branch and the sharp bound $\tildeα^2\mathcal R_{abcd}\mathcal R^{abcd}<28$ for nonnegative mass. For initially untrapped five-dimensional spherical data with a regular center, a bound on $K$ alone ensures smooth continuation on compact domains of dependence, so any first characteristic loss occurs on a smooth background, and a marginal sphere formed before any loss forces a later loss. Complete smooth data form marginal spheres at every allowed radius with mass arbitrarily close to its sharp lower bound; in six dimensions radius and mass can both be arbitrarily small. Without spherical symmetry, complete initial data with weak curvature contain, at sufficiently large scale, outermost strictly stable marginal surfaces with prescribed $S^3$ geometries satisfying a spectral condition; Berger surfaces among them have arbitrarily small area at fixed mass. Their formation from untrapped data is left open. Near a contracting homogeneous core, exact nonspherical developments of smooth constrained data converging with every derivative have bounded curvature but, after the core's characteristic loss, a fixed discrepancy in a geometric tidal record. Classical existence, local geometric uniqueness and continuity of this pointwise record cannot all be guaranteed on a common observation region. A companion paper treats narrow incoming pulses.