Falcon 50 First Officer reported an uncommanded leading edge slat deployment; accompanied by an audible stall warning; a red light on the slat indicator. The flight crew diverted to the nearest suitable airport.

Narrative

On Day 0 at approximately 3.5 hours into a flight from ZZZ2 to ZZZ3 our Falcon 50 had an uncommanded leading edge slat deployment. It was accompanied by an audible stall warning; a red light on the slat indicator. Autopilot was on in level flight; .82 Mach. FL400. I was in the right seat and pilot monitoring (PM). I had my seat back because I had just finished lunch and hadn't adjusted forward yet. The pilot flying (PF) disconnected the Autopilot and applied stall correction and then started a descent and retarded the throttles to keep the speed appropriate. I pulled my seat forward to assist and saw he was initiating a descent so I began with letting ATC know we were requiring an immediate descent; my crew member indicated he was taking over the calls and repeated our request and asked for an immediate descent. PF took over radios from that point and re-iterated to ATC we weren't a priority aircraft because we had things under control.I pulled the checklist and went to look at the aft diagram for the item number; while I was looking the PM told me he didn't think was a checklist for this problem. I wasn't sure that was true and looked at the page I saw listed. It had air brakes and auto slats checks listed. Later when reviewing the situation after the event I saw I had missed the next page attached to this event. We discussed manual deployment and that helped the situation. We then had a green deployed light and the horn was silenced.We had requested closest appropriate airport and were head for ZZZ1 by ATC. Reprogramming the FMS; reviewing normal checks and reviewing the airport followed.I brought up runway length and asked if ZZZ might be a better option due to longer runways if we had any other issues. We checked weather at both places and they were similar but ZZZ was a little further out. We reviewed fuel and burn and both were above limits and acceptable. We asked to turn for ZZZ for the longer runway and received clearance. Reset FMS and reviewed approaches and weather.PF wanted to clean up and see if we could reset the system. His reasoning was we could be more efficient and less fuel burn. Everything cleaned up and we flew at 15000 towards ZZZ at 250 kts. We had a moment so I notified base we had an uncommanded slat deployment and we were diverting to ZZZ. They asked about ZZZ3 and we responded unable. ZZZ4 for Maintenance support. We looked and it was 14 miles difference from our current position. The weather wasn't as good but well above minima on an ILS so we agreed and let ATC know.We reset everything and headed there and were on the arrival when we started getting another slat deployment at 11;000 feet near ZZZZZ. It created a left rolling and we deployed the slats manually which corrected the issues. We proceeded to landing. Safe landing; full flaps.After landing; Maintenance was able to trouble shoot a bad AOA and a possible contributing factor of hydraulic leak.