updated 12/03/2012 AT 3:00 PM ET
•originally published 12/03/2012 AT 4:00 PM ET
Following the announcement of an upcoming addition to the royal family, Prince William was photographed leaving the King Edward VII Hospital in Central London where a pregnant Kate was admitted for acute morning sickness on Monday.
Kate – who is in the “very early stages” of her pregnancy, according to the Palace – has been diagnosed with hyperemesis gravidarum, characterized by severe and persistent nausea and vomiting during pregnancy.
Wearing a grey sweater, William is seen exiting the hospital and heading toward a waiting vehicle.
While a source at St. James’s Palace tells PEOPLE that the couple decided to “be open” about Kate’s pregnancy because she was admitted to the hospital, Kate, 30, and William, 30, “aren’t going into detail about the pregnancy itself.”