git: list new files only

The commands below no longer give the expected results, I may originally also have made some mistakes. Please double-check your output and the options you are using. Nevertheless: The basic tenet of using diff-filter should still hold true.

Don't use grep to parse git output. Git almost certainly has the things you are looking for built-in (except if you are going for really advanced stuff).
You can use git diff to show the changes. --name-only shows only the filenames. --diff-filter=A lists only the added files.
If you want to see new files you have already added to the index use --cached, otherwise omit it. To see both diff to HEAD.
The commands look like this:

git diff --name-only --diff-filter=A --cached # All new files in the index  
git diff --name-only --diff-filter=A          # All files that are not staged  
git diff --name-only --diff-filter=A HEAD     # All new files not yet committed

Instead of parsing the output of "git status", it is probably more elegant to use

git ls-files -o  --exclude-standard

As with git status, ls-files will produce output relative to your currrent working directory.

You may wish to include the --full-name option:

git ls-files -o  --exclude-standard --full-name

You can use git status --short to get the list of files.