ticket で null が帰ってきてしまうよ。 
private int loginApp(String mail,int pass){
 URL loginURL;
 try {
 loginURL = new URL("https://secure.nicovideo.jp/secure/login?site=nicolive_antenna");

 URLConnection con = loginURL.openConnection();
 con.setDoOutput(true);

 PrintWriter out = new PrintWriter(con.getOutputStream());
 out.print("mail=" + mail + "\npassword=" + pass);
 out.close();

 InputStream inputStream = con.getInputStream();
 DocumentBuilder docBuilder = DocumentBuilderFactory.newInstance().newDocumentBuilder();
 Document document = docBuilder.parse(inputStream);

 Element rootElement = document.getDocumentElement();
 Attr authTicket = rootElement.getAttributeNode("ticket");

 System.out.println(authTicket);

 } catch (MalformedURLException e) {
 e.printStackTrace();
 } catch (IOException e) {
 e.printStackTrace();
 } catch (ParserConfigurationException e) {
 e.printStackTrace();
 } catch (SAXException e) {
 e.printStackTrace();
 }


 return 0;
 }