Generalizing Digitization to Curved Spacetime

In earlier work, a mechanism was established whereby a continuous Born-Infeld (BI) field in flat spacetime gives rise to discrete, particle-like objects. A critical question is whether this mechanism is merely an artifact of the flat-space approximation or if it survives within a complete theory of gravity, where the energy of the fields acts as a source for spacetime curvature. This document attempts to demonstrate the generalization to a curved background by analyzing the solutions to the coupled Einstein-Born-Infeld system.