AN LJ45 HAD AN ENG FIRE WARNING WHILE ON SHORT FINAL. NO EMER WAS DECLARED. UPON POST FLT INSPECTION; A CHARRED SPOT WAS FOUND ON ENG COWLING; ALONG WITH HYD FLUID LEAKING FROM THE ENG.

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ON SHORT FINAL; WE RECEIVED A 'L ENG FIRE' WARNING. ALL ENG INST INDICATIONS WERE NORMAL. I REDUCED PWR ON THE L ENG AND WE ELECTED TO CONTINUE THE APCH AND LNDG. THE LNDG WAS NORMAL AND UNEVENTFUL. AFTER CLRING THE RWY; WE SHUT DOWN THE L ENG. THE FIRE WARNING EXTINGUISHED SHORTLY (LESS THAN 30 SECONDS) AFTER THE ENG WAS SHUT DOWN. THE TAXI TO THE RAMP WAS NORMAL AND UNEVENTFUL. AFTER SHUTDOWN OF THE ACFT; THE POSTFLT INSPECTION REVEALED HYD FLUID LEAKING FROM THE BOTTOM OF THE L ENG. THERE WAS ALSO A CHARRED SPOT ON THE LOWER; FORWARD; R SIDE OF THE L ENG COWLING. WE DID NOT DECLARE AN EMER; AS THE EVENT HAPPENED ON SHORT FINAL INTO AN UNCTLED ARPT AND OUR ONLY COM WAS ON THE LCL CTAF. WE DECIDED THAT THE LNDG WAS SAFER THAN A GAR ON SHORT FINAL WITH A POSSIBLE ENG FIRE AT AN UNCTLED FIELD WITH OTHER TFC IN THE AREA. LEARJET MAINT PERSONNEL ARE STILL INVESTIGATING THE CAUSE OF THE FIRE. IT IS SUSPECTED THAT A PINHOLE IN A HYD LINE SPRAYED HYD FLUID ON THE STARTER/GENERATOR TO START THE FIRE. HOWEVER; THE INSPECTION OF THE ENG IS STILL UNDERWAY. SUPPLEMENTAL INFO FROM ACN 654199: THERE HAVE BEEN NUMEROUS FALSE FIRE INDICATIONS IN THE LEARJET 45 DUE TO 2 COMMON PROBS WHICH ARE: 1) BLEED AIR LEAK; 2) CHAFED FIRE LOOP. AT THIS POINT THERE IS AN INVESTIGATION ONGOING TO FIND WHAT CAUSED THE PROB; AND I'M VERY EAGER TO FIND OUT WHAT CAUSED THE FIRE; BUT AT THIS TIME I WILL NOT ASSUME THAT IT IS BLEED AIR LEAK OR A CHAFED FIRE LOOP IF I GET A 'L OR R ENG FIRE' WARNING AGAIN.