Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Flight Crew Became Reoriented
Human Factors; Environment - Non Weather Related
About 20 DME southwest of SAV ATC told us to descend to 2000. About the same time we received an ATC caution terrain warning ATC told us to climb to 2500.
We were giving direct to the Outer Marker (OM) for a visual. At 5000 feet we received a TCAS warning from a [aircraft] doing aerobatics. ATC advised of traffic to our right and climbing fast. I saw him climb and do a snap roll then a couple of knife edges which is when I believe he saw us. After that we were given a descent to 2000 feet. PIC started a descent to 2000 feet from 5000 feet. Although it was haze we began to see two antennas in front of us which seemed very high. At the same time we both saw them appear on the terrain avoidance map on the MFD. In the next couple of seconds we received a caution terrain message. A few second after that we got an ATC climb to 2500 feet. We climbed to 2500 feet to avoid the antennas. From this point we had the airport in sight and were cleared for a visual approach to 10. No other mention of this was made from ATC.
Flight crew reported receiving a low altitude warning while approaching the SAV area.