Is it permissible for a bodybuilder to show his picture to his friends while he is bare-chested, with part of his abdominal muscles (above the navel) showing, and covered from the navel down to his feet?

The 'awrah of a man, which he must cover, is from the navel to the knee, based on the Prophet's (peace be upon him) saying: "What is between the nav navel and the knee is 'awrah." There is no harm in exposing what is not part of the 'awrah, though it is recommended to cover it and disliked to uncover it.