Normally, when you rebase another author's commit with git, git adds a Commit:
header with your name and email address. I have a situation where I don't want this to happen. I want the rebased commit to end up with the same SHA1 as it would have if the original author had done the equivalent rebase him/herself. Is this possible?
All git commits have a committer field internally; you can see this by typing git cat-file commit HEAD
immediately after committing something. As such you cannot erase it; you can only make it equal to the author field.
That said, you might be seeing git porcelain showing the commit field because the datestamp has changed. It's not possible to predict what someone else would get for the commit datestamp if they were rebasing, obviously, but you can alter it to be equal to the original commit timestamp, at least.
git filter-branch --commit-filter 'export GIT_COMMITTER_NAME="$GIT_AUTHOR_NAME"; export GIT_COMMITTER_EMAIL="$GIT_AUTHOR_EMAIL"; export GIT_COMMITTER_DATE="$GIT_AUTHOR_DATE"; git commit-tree "$@"' -- basecommit..HEAD
This will alter commits after basecommit, in the history of HEAD (including HEAD, not including basecommit), making their committer field identical to the author field in all respects. If the original author agrees to do the same thing, then you can get a consistent SHA1.