Numerical Simulation for General Relativistic Magnetohydrodynamics in Dynamic Spacetimes

We present a novel spectral solver for general relativistic magnetohydrodynamics on dynamical spacetimes. By combining a high order discontinuous spectral method on mapped Chebyshev Fourier grids, our scheme attains exponential convergence. Implemented within a unified BSSN Valencia framework, the code evolves both Einstein and MHD fields self consistently, enabling fully coupled simulations of black hole accretion jet systems. We demonstrate spectral accuracy and entropy stability through convergence tests, and validate physical fidelity via equatorial embedding diagrams of horizon crossing GRMHD variables in Kerr Schild coordinates. Three dimensional scatter visualizations further highlight the solver's capability to capture complex magnetized plasma structures around rotating black holes. This approach paves the way for high order, low dissipation GRMHD simulations on exascale architectures, opening new avenues for precise modeling of strong field astrophysical phenomena.