  We show how to transform a Dirac equation in curved spacetime into a Dirac
equation in flat spacetime. In particular, we show that any solution of the
free massless Dirac equation in a 1+1 dimensional flat spacetime can be
transformed via a local phase transformation into a solution of the
corresponding Dirac equation in a curved background, where the spacetime metric
is encoded into the phase. In this way, the existing quantum simulators of the
Dirac equation can naturally incorporate curved spacetimes. As a first example
we use our technique to obtain solutions of the Dirac equation in a particular
family of interesting spacetimes in 1+1 dimensions.
