What was found
(CAN) ON INITIAL CLIMB, HEARD A SUDDEN AND LOUD NOISE BETWEEN 4000 AND 4500 FT AND THE RT ENGINE SHUTDOWN ITSELF IN FLT. AFTER ASSESSING THE SITUATION AND FOLLOWING QRH AND MEMORY ITEMS, THE CREW NOTIFIED THE FLT ATTENDANT, PAX AND MX OF THE SITUATION. AN EMERGENCY WAS DECLARED AND THE CREW PROCEEDED TO DIVERT BACK TO PLACE OF DEPARTURE. AN UNEVENTFUL LANDING FOLLOWED. MX REPLACED THE RT ENGINE.