When you say this:

$about_window->set_url_hook(open_browser($url));
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You're calling set_url_hook with as parameter the result of open_browser($url). I'm not familiar with Gtk2, but you probably want something like

$about_window->set_url_hook("open_browser",$url);
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i.e. you tell set_url_hook the name of the function to call; it's possible that you have to pass the argument to open_browser in a different way; you'll have to experiment or read the docs to find out.