In this paper we prove small data global existence for solutions to the Maxwell--Born--Infeld (MBI) system on a fixed Schwarzschild background. This system has appeared in the context of string theory and can be seen as a nonlinear model problem for the stability of the background metric itself, due to its tensorial and quasilinear nature. The MBI system models nonlinear electromagnetism and does not display birefringence. The key element in our proof lies in the observation that there exists a first-order differential transformation which brings solutions of the spin $\pm 1$ Teukolsky equations, satisfied by the extreme components of the field, into solutions of a "good" equation (the Fackerell--Ipser Equation). This strategy was established in [F. Pasqualotto, The spin $\pm 1$ Teukolsky equations and the Maxwell system on Schwarzschild, Preprint 2016, arXiv:1612.07244] for the linear Maxwell field on Schwarzschild. We show that analogous Fackerell--Ipser equations hold for the MBI sy 查看全文>>