If gravitons exist (Gravity can be explained with a quantum theory), then gravitational waves would consist of gravitons.However, real gravitons propagate away to infinity, as oscillations on the gravitational field. This is what LIGO detected. (And real photons propagate away to infinity, as oscillations on the electromagnetic field. This is what telescopes detect.)
LIGO detected gravitational waves as predicted by EFE not gravitons. Gravitons are theorized to exist and have such low energy levels that we can not detect them with todays technology.
Gravitons can't, but since gravity would be mediated by virtual gravitons, this is no different from the fact that photons can't escape a BH, yet a BH can have a charge and an electromagnetic field mediated by virtual photons.
Bosons can not escape a BH, a graviton is a 2 spin boson how can it get out of a BH. A gamma ray cannot escape the event horizon of a BH and it has significantly more energy.
Gravitational waves definitely exist gravitons might not exist, and might not have enough energy to escape a BH.Gravitational waves can't escape a BH either (By this I mean that gravitational waves cannot get out from inside the event horizon anymore than electromagnetic waves can.)
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