Law enforcement sources tell us ... John passed away Friday in San Antonio, this after he was discovered unresponsive in a hotel room. We're told no foul play is suspected at this point, and the cause of death is pending an autopsy.

The family broke the news through a rep, saying ... "With a heavy heart, Gordon Getty announces the death of his son, John Gilbert Getty." The spokesperson adds, "John was a talented musician who loved rock and roll. He will be deeply missed."

John's other brother, Andrew, died in 2015 from meth intoxication ... and his own, mother, Ann, died from a heart attack just this past September.

John Gilbert was one of several descendants of J. Paul Getty -- the oilman whose art collection served as the basis for the Getty Museum in L.A. Not too much is known about JG other than the fact he bounced around in L.A. ... jumping from one multi-million-dollar home to the next, and that he was apparently pals with Gov. Gavin Newsom.

The Getty family fortune is estimated to be north of $5 billion these days -- and there are still several living heirs between children, grandchildren and great-grandchildren.

John Gilbert is survived by his daughter, Ivy Getty, and his brothers, Peter and Billy.

He was 52.