Gravity alters time, this has been proven on tall sky scrapers, where the clocks on the top floors and bottom floors even when synced up slowly separate. CERN has reported to produce black holes, so if they can harness them somehow then they could theoretically make a time machine. They're smart people, I would bet that they already have one or are working on one.

People would freak out if they announced they were testing time travel and had to admit it involved black holes. They would have to keep it under-wraps until it was working perfectly.