There is a research station at the south pole (manned by the US?).
What is the local time there? All time zones converge at the poles so I assume its Washington time.
Presumably they use GMT. That would make things simpler for scientists.
I sent a similar question to Cecil once. “What time is it at the North Pole”
It never got answered. 
The South Pole runs on the same time zone as New Zealand, since most incoming flights come from there. See here. Other places in Antarctica would, I assume, use their longitude to determine their time zone; but obivously this wouldn’t work for the South Pole.