What was found
MX PERFORMED AN ADJUSTMENT ON THE FUEL DENSITY AND IDLE RPM ON THE LT ENGINE, WHICH REQUIRES A MAX ALTITUDE ACCELERATION CHECK IAW THE MM CHAP 72-00. FLIGHT CREW LT RDU FOR THE PURPOSE OF PERFORMING THIS CHECK. FLIGHT CREW CLIMBED AND STARTED THE CHECK AT FL410 FIRST AS CALLED OUT IN THIS PROCEDURE. THE CHECK PASSED WITH NO ISSUES AT FL410. FLIGHT CREW PROCEDED TO CLIMB TO FL450 IAW THE REQUIREMENTS OF THE CHECK. UPON CLIMBING THROUGH FL443, THE RT ENGINE FLAMED OUT. FLIGHT CREW INITIATED A DESCENT INTO THE ENVELOPE FOR AN AIRSTART. CREW LEVELED AT FL200 AND PERFORMED AN AIRSTART ON THE RT ENGINE. RT ENGINE STARTED UP NORMALLY AND THE FLIGHT CREW PROCEDED BACK TO AND LANDED AT RDU WITH NO FURTHER OCCURENCES. MX LIMITED THE MAX ALTITUDE TO FL410 IAW THE MM 72-00, FIG 509 AND INSTALLED PLACARDS NEXT TO THE PILOTS AND COPILOTS ALTIMETERS STATING "DO NOT CLIMB ABOVE FL410".