This question already has an answer here:
What defines the service ceiling for aircraft, in particular the F-16?
I suppose, as with almost everything, this depends on the aircraft, the engine type, etc. While I'm fine with a comprehensive answer including some discussions for different types of aircraft, I'm just limiting this to the F-16 to make it specific enough.
Basically, what exactly is it that prevents the F-16 from exceeding 50,000 ft?
Imagine an F-16 at 50,000 ft in a clean configuration, full afterburner, having reached around mach 2, then the aircraft attempts to climb at maximum rate of climb.
What will happen?
Is the engine unable to ingest enough air? Making the air fuel mixture too lean, eventually resulting in flameout or damage to the engine?
Is it due to the aircraft being unable to produce enough lift at this altitude? How much lift does an F-16 need anyway? Within a certain envelope, the thrust to weight ratio of the F-16 supposedly exceeds 1 and the aircraft can climb vertically -- however, I don't imagine this to hold true for very high altitudes, probably only within an narrow optimal set of parameters?
Is it a combination of the two? Which hits the F-16 first?