GIT_DIR question

I wanted to create cloned repo, but with metaninfo separately from data.
I cloned the repo ( git-clone ~/repo ~/x) ,
then I moved ~/x/.git to different place (mv ~/x/.git ~/git);
then exported GIT_DIR=~/git; then
cd ~/x;
But now 'git status' says 'fatal: runstatus must be run in a work tree' . Why ?

'ls $GIT_DIR'  shows
  FETCH_HEAD  HEAD  ORIG_HEAD  branches  config
  description  hooks  index  info  logs  objects  refs
This is ok, no ?

Thanks
Yakov