Jet pilot conducting a visual approach at night they experienced CFTT event and received a low altitude alert from ATC.

Narrative

During descent down to the cleared altitude of 8;000 ft. ATC kept asking us if we had ZZZ in sight. Like they just wanted to get rid of us. As soon as we called it in sight; we were cleared down to 6;000 ft. and told we were 'cleared for the visual' contact ZZZ Tower. The ARTCC controller may have given us improper clearance down to an unsafe altitude ! I proceeded westbound to basically fly a base leg for Runway XXL. We seemed high so we slowed; added slats and 20 degrees of flaps and were using the airbrakes to slow; descend and turn for the runway. I overshot the runway centerline while a few miles out thinking I had more altitude to lose. Then my co-pilot; asked something. I said 'standby - I'm looking at a black hole here' My co-pilot looked up from whatever he was doing and immediately said 'MOUNTAINS - CLIMB!!!' I IMMEDIATELY ADDED POWER; CLOSED THE AIRBRAKES AND PROCEEEDED TO CLIMB. A few moments later; while already climbing; ATC called our 'N' number and said 'LOW ALTITUDE ALERT' to which I responded CLIMBING. We received NO GPWS ALERT from the airplane. I reported this to company for them to have avionics and maintenance look into the matter.We continued the Visual Approach after clearing past the mountains and continued to complete a safe landing. In hindsight: my conclusion and lesson learned. ALWAYS request and fly an instrument approach in mountainous terrain especially at night ! All of this happened after a long day; last leg when we were tired and during the flight the autopilot had broken making us descend out of RVSM airspace and handfly the aircraft for the last hour and half of the flight.