updated 07/11/2012 AT 10:00 AM ET
•originally published 07/11/2012 AT 10:30 AM ET
However, the star, 50, made a public statement of his own Tuesday, when he was back to work on the June Lake, Calif., set of Oblivion – without his wedding ring.
Talking to a photographer before filming the final scene of the day, a dressed-down Cruise – who will have generous visitation rights – wore no band on his left hand. Holmes, 33, was first spotted without her ring when she filmed Project Runway: All Stars July 2, just days after news broke of their split.