  It is well-known that parity symmetry is broken in the weak interaction but
conserved for Einstein's general relativity and Maxwell's electromagnetic
theory. Nevertheless, parity symmetry could also be violated in the
gravitational/electromagnetic sectors if a fundamental scalar field couples to
the parity-violating gravitational/electromagnetic curvature terms. Such
parity-violating terms, which flip signs under reversed spatial directions, can
inevitably lead to a negative effective mass squared for the scalar field
perturbations near nonspherically symmetric black holes and thus are expected
to trigger tachyonic instability. As illustrative examples, we show that the
scalar field coupled to gravitational/electromagnetic Chern-Simons terms near a
Kerr-Newmann spacetime can develop tachyonic instabilities, leading to
equilibrium scalar field configurations in certain parameter regions of black
holes. This instability, which is an indication of the black hole scalarization
process, can occur in a broad class of nonspherically symmetric black holes and
parity-violating theories.
