B757 Undifferentiated or Other Model
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Engineer
Flight Crew Last 90 Days 65; Flight Crew Total 12767; Flight Crew Type 6370
Situational Awareness
Flight Deck / Cabin / Aircraft Event Illness / Injury; Inflight Event / Encounter CFTT / CFIT
Flight Crew Took Evasive Action; General Declared Emergency
Human Factors
During Medical emergency diverting into ZZZ received momentary Terrain caution alert followed by pull up due to not being configured for landing. We were coming over ZZZ1 direct ZZZ and about 50 miles out were cleared to the 12 mile final fix for rwy X.  ATC cleared us to 110 where were started slowing to 250 for further descent. Visibility was unrestricted with partial moon light and we could see our route took us through the saddle in the ridge south of the airport. MSA was 10.5 and 10-1 page showed 7000 foot terrain line 10 miles east of rwy X centerline with the terrain indicating 7-9 thousand feet where we were going to track across the ridge. The terrain causing our msa of 10.5 was clearly south of us visually and confirmed on the terrain display.  We had the airport in sight and verbally pointed out the airport beacon and ramp lights associated with the location to the town about 30 miles out. At about 20 miles out atc asked if we had airport in sight and cleared us a visual to rwy X when we said yes. We then turned direct the 6 mile final fix and when mountain ridge was clearly down below our nose I started descent to 10.5 and subsequently descended toward 9000 when terrain looked clear. At about 9500 ft and descending less than 1000 fpm we received a terrain caution alert most likely due to radar altimeter sensing a rapid terrain closure due to some ridges below. terrain map showed no green or amber in our flight path and some green several miles to the south confirming our visual cues outside. This was followed by a pull up aural due to terrain proximity sensed when not configured to land. Since it was not day vmc we complied by initiating the terrain avoidance maneuver at which point the warnings immediately ceased.  We reverified our position to the field visually and with instruments (alt; ra;terrain map;hsi) and slowed and configured then continued descent to landing with no further cautions. I understand the extra vigilance and altitude awareness required when flying at night but due to the medical emergency decided the visibility and time constraints warranted a short approach (3 mile final) rather than vectors to final.  In hind sight I should have slowed and configured prior to descending out of 10.5 as the green page describes for rwy 26;  or just waited for an atc controlled descent to final. I do not believe we were ever closer than 2000 feet to terrain till turn to final except for a momentary ridge that may have approached 1000 ft agl tripping the terrain caution. Descent rate was never excessive but the closeness to the ridge sensed high closure rate through the ra causing the alert.
B757 Captain reported receiving a GPWS terrain alert on a night visual approach to an airport with higher terrain in the area.