url rewriting - rewrite url for authors

I have been struggeling with this for a while now and can't seem to get this to work. What i want is the following.

I create a custom slug for authors with

$slug = sanitize_title( $author->first_name . $author->last_name );

Then i want to have domain/$slug to show the author page of that author/user. Im trying to do this as followed:

add_filter( 'author_rewrite_rules', 'no_author_base_rewrite_rules' );

function no_author_base_rewrite_rules( $author_rewrite ) {
    global $wpdb;
    $author_rewrite = array();

    $authors = get_users();

    foreach($authors as $author) {
        $slug = sanitize_title( $author->first_name . $author->last_name );

        $author_rewrite["({$slug})/?$"] = 'index.php?author_name=' . $author->nicename;
    }

    return $author_rewrite;
}

But i can't get this to work. Anyone has a idea how i can get this to work properly?

Thanks in advance!