New approach to the calculation of particle creation from analog black holes

Accurate prediction of particle creation from accelerating mirrors is crucial for interpreting forthcoming analog Hawking radiation experiments such as AnaBHEL. However, realistic experimental setups render the associated Bogoliubov integrals analytically intractable. To address this challenge, we introduce the Inertial Replacement Method (IRM), a hybrid analytic-numerical framework for computing Bogoliubov coefficients for general moving-mirror trajectories. The IRM replaces the asymptotically inertial portions of a trajectory with analytic inertial extensions, so that numerical evaluation is required only for the finite accelerating segment. We derive perturbative error bounds for both perfectly and imperfectly reflecting mirrors, providing controlled accuracy estimates and guiding the choice of segmentation thresholds. The method is validated against analytically solvable trajectories and then applied to a fully numerical, PIC-based Chen-Mourou plasma-mirror trajectory relevant to the planned AnaBHEL experiment. A key physical insight emerging from this analysis is that the radiation spectrum is determined almost entirely by the finite accelerating region, with negligible sensitivity to the far-past and far-future inertial motion. These results establish the IRM as a reliable and broadly applicable computational tool for modeling particle creation in realistic analog-gravity systems such as AnaBHEL.