  The main objective of this work is to present a theoretical proposal for an
implementation of the $(2 + 1)$-dimensional Dirac equation in classical
gravitational and electromagnetic backgrounds in a two-dimensional waveguide
array. For this, a framework for achieving site-dependent effective coupling
constants in two-dimensional waveguide arrays is developed. Implementability of
the Dirac equation under the proposed scheme puts minor demands on gauge and
spacetime backgrounds; however, a wide array of physical spacetimes, such as
all vacuum and static solutions, prove to be implementable. As an interesting
and instructive example, we discuss a tabletop realization of the gravitational
Aharonov-Bohm effect: After devising a thought experiment in which signatures
of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss
how the analogue of such a setting can in principle be implemented using the
proposed waveguide setup.
