 The paper analyzes an optical Fabroparo resonator as a time-periodic driving of the 2D optical field, revealing that resonator twist produces a synthetic magnetic field while mirror aberrations produce relativistic dynamics and harmonic trapping and spacetime curvature. A flow-K formalism is developed to compute the effective Hamiltonian for the 2D field, generalizing the idea that the intracavity optical field corresponds to an ensemble of non-interacting, massive, harmonically trapped particles, highlighting the potential of optical resonators for exploring quantum fluids in gauge fields and exotic spacetimes. This article was authored by Ariel Sommer and Jonathan Simon.