open-current-git-top-directory-in-tmux-new-pane.el

(defun git-top-directory ()
  (file-name-as-directory
   (replace-regexp-in-string
    "\n" ""
    (shell-command-to-string "git rev-parse --show-toplevel"))))

(defun open-current-git-top-directory-in-tmux-new-pane ()
  (interactive)
  (let ((top-dir (git-top-directory)))
    (unless (file-directory-p top-dir)
      (setq top-dir ""))
    (let* ((dir top-dir)
           (cmd (concat "tmux split-window -v \"cd " dir "; exec $SHELL\"")))
      (cond ((eq (shell-command cmd) 0)
             (message "Open directory %s in tmux new pane." dir))
            (t
             (message "Failed to create new pane in tmux."))))))

(global-set-key (kbd "M-t") 'open-current-git-top-directory-in-tmux-new-pane)