Send email to admin with post author

by

Missing global ?

global $post;

No global variable available if you are using publish_post action hook!

Ref : http://hungred.com/how-to/tutorial-post-id-publishpost-action-hook-wordpress/

Update 2 :

or try this

$author = get_userdata($post->post_author);

So you can use $author where you will 😀