Stephen Hawking, theoretical physicist, is in Extremely Loud and Incredibly Close for several reasons. One reason is that his letters are the metaphorical window (or mirror) through which we see Oskar's perpetual feelings of disappointment and longing. These apply outright to Hawking but also apply symbolically to Oskar's father. Another reason is to provide an ironic counterbalance to that which is extremely loud and incredibly close. Hawking's work has to do with the cosmos, which is definitely something other than loud and close, and it has to do with quantum particles, which are also the opposite of loud and close.
One of the most interesting reasons that Stephen Hawking is in Foer's book is that Hawking provides Oskar with a metaphoric substitute for his father, because things Oskar loves most about his father are the way his mind works and the way their conversations and searches work because of how his mind works. Stephen Hawking is celebrated for the way his mind works, which makes him an extremely credible substitute for his father after the events of the "worst day."
After that "worst day," when Oskar began writing letters and mailing them with the stamps he had at hand, which included his valuable collected stamps, he sent a letter to Stephen Hawking asking, "Can I please be your protégé?" With his father incredibly far away now, forever away, being Hawking's protege would provide comfort and would allow the conversations (Oskar imagined...) and searches to continue. Oskar unconsciously felt (because his boots got lighter) that being the protégé of Hawking's extremely wonderful mind would be like being the son of his dad's extremely wonderful mind.
I started writing lots of letters, ... [I]t was one of the only things that made my boots lighter. ... The first letter I wrote was to Stephen Hawking. I used a stamp of Alexander Graham Bell.
One answer to this question may be that while Stephen Hawking is dedicated to explaining things that are silent (particles) and very far away (cosmos), which is the opposite of this book's title, I think there are several reasons why his appearance is important to this text. It becomes apparent that Stephen Hawking is an idol for Oskar. He's read his famous "A Brief History of Time," watched lectures, and even written to the revered scientist. One comparison between Hawking and Oskar would be their shared difficulty in communicating. While Hawking has a physical condition that limits his ability to communicate without the help of his computer, Oskar has a problem with communicating with others as well, though his is more mental/psychological than physical. Hawking's computer doesn't really allow for change in inflection/emotion. He basically sounds like a robot. Sometimes, Oskar acts like a robot because he can't express himself. Yet they both have beautiful minds. Oskar sometimes has trouble understanding the immediate world around him (home, school, etc), and looks to science because it can be explained through equations and papers, so it is understandable that he would be attracted to Hawking. They are both unique people trying to navigate their way through the world. Hawking also serves, in some ways, as a replacement of Oskar's father, yet the two are very different. Hawking is concerned with the cosmos, seeing humans as just small specks in the vast universe. One person's life does not matter much in comparison to entire universe. However, Oskar's father believes that every life is significant, and spends time trying to instill that belief in his son. He wants Oskar to know he's worth something, a concept that is difficult for Oskar to believe when he lets his mind wander to the grander ideas of the universe. Oskar loves his father, and when he loses him, he reaches out to Hawking for support. Unfortunately, Hawking's response is cold and distant. Oskar branches out from his letter to Hawking and goes on a quest to connect with people all over the city. There are more letters and house calls as he travels through the boroughs of New York City. The event that serves as a catalyst for this story, 9/11, also proves how significant each life is. There were only a few hijackers on the planes, and yet they killed thousands, which impacted millions and billions across the globe, the effects of which are still being felt today. Though he is one child, Oskar affects everyone he comes in contact with (by getting extremely loud and incredibly close sometimes). His pure existence negates the idea that individual lives are insignificant.