  We show how the universal low-energy properties of Weyl semimetals with
spatially varying time-reversal (TR) or inversion (I) symmetry breaking are
described in terms of chiral fermions experiencing curved-\emph{spacetime}
geometry and synthetic gauge fields. By employing Clifford representations and
Schrieffer-Wolff transformations, we present a systematic derivation of an
effective curved-space Weyl theory with rich geometric and gauge structure. To
illustrate the utility of the formalism, we give a concrete prescription of how
to fabricate nontrivial curved spacetimes and event horizons in topological
insulators with magnetic textures. Our theory can also account for
strain-induced effects, providing a powerful unified framework for studying and
designing inhomogeneous Weyl materials.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons;Quantum Physics