Simulation of the massless Dirac field in 1+1D curved spacetime

Simulating the nature of quantum fields in diverse spacetime backgrounds offers valuable insights for the fundamental comprehension of quantum mechanics and general relativity. Here we introduce a novel method for mapping the massless Dirac equation in 1+1D curved spacetime to a controllable quantum simulation model, applicable to various observers’ perspectives. We perform numerical simulations of Simpson spacetime and calculate tunneling rates in Painleve and Schwarzschild coordinates, which align closely with theoretical predictions of Hawking radiation. Additionally, we show the transition of Simpson spacetime from a regular black hole to a wormhole as the parameter $\mathrm{"}a>r_s\mathrm{"}$. This method facilitates the study of spacetime from various coordinate perspectives (observers), providing deeper insights and understanding.