He's not flying NASA's Vomit Comet, another company has been operating a similar aircraft (and flight profile) for several years that anyone can buy a ticket on. They're giving Hawking his ride for free.
http://news.com.com/Stephen+Hawking+plans+prelude+to+the+ride+of+his+life/2100-11397_3-6163473.html?tag=newsmap
http://news.com.com/Stephen+Hawking+plans+prelude+to+the+ride+of+his+life/2100-11397_3-6163473.html?tag=newsmap