  We study the evolution of heavy stars ($M\ge40{\rm M}_\odot$) undergoing
pair-instability in the presence of annihilating dark matter. Focusing on the
scenario where the dark matter is in capture-annihilation equilibrium, we model
the profile of energy injections in the local thermal equilibrium
approximation. We find that significant changes to masses of astrophysical
black holes formed by (pulsational) pair-instability supernovae can occur when
the ambient dark matter density $ \rho_{\rm DM} \gtrsim10^9 \rm \, GeV \,
cm^{-3}$. There are two distinct outcomes, depending on the dark matter mass.
For masses $m_{\rm DM}\gtrsim1$ GeV the DM is primarily confined to the core.
The annihilation increases the lifetime of core helium burning, resulting in
more oxygen being formed, fueling a more violent explosion during the
pair-instability-induced contraction. This drives stronger pulsations, leading
to lighter black holes being formed than predicted by the standard model. For
masses $m_{\rm DM}\lesssim0.5$ GeV there is significant dark matter in the
envelope, leading to a phase where the star is supported by the energy from the
annihilation. This reduces the core temperature and density, allowing the star
to evade the pair-instability allowing heavier black holes to be formed. We
find a mass gap for all models studied.
