Air carrier departure climbing with ZJX received TCAS RA from VFR military high performance aircraft in a rapid descent; traffic was issued by ATC.

Narrative

We received clearance to deviate east of our flight plan due to weather conditions. We were southeast of SAV VORTAC with clearance to proceed directly to CHS when clear of the weather. ZJX Center issued clearance to climb to FL230. Climbing through 15;800; Center reported a VFR military fighter in a descent through 16;800 at the 11:00 position to us. However; we did not have the aircraft in sight at that time. Within seconds we received a TCAS traffic alert; immediately followed by a RA descend. My First Officer followed the RA descent command and descended to 15;200. At the same time I reported the RA descent to Center. Center then gave us a heading change of 15 degrees right. Seeing that the entire event happened within a few seconds; we were unsure that the military jet ever had us in sight. The VFR aircraft descended through our flight path during our climb. I believe that high performance aircraft operating under VFR operations limits pilots and controllers the advantage of reaction time. If certain limits were in place; then reaction time would be increased for both pilots and controllers to see and avoid a collision.