Structure of the Cauchy horizon for the 3D relativistic Euler equations with vorticity and entropy

Under the assumptions of the time-of-first-blowup conjecture, let the background solution have a Cauchy horizon, and let the corresponding perturbed Cauchy horizon be defined for the perturbed solution. The background and perturbed solutions are those arising from smooth initial data close to a simple isentropic plane-symmetric background solution.

Cauchy-horizon conjecture. The perturbed solution has a Cauchy horizon that is a perturbation of the Cauchy horizon of the background solution.

This conjecture predicts stability of the Cauchy-horizon geometry under general perturbations of the background flow, including vorticity and entropy. The source illustrates the background and conjectured perturbed horizons in the associated figures, but does not establish the relativistic assertion.