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.
On set, Cruise stayed to himself, a source tells PEOPLE. (Shooting is expected to go through this week in the mountains.)
Meanwhile, Holmes was spotted with Suri at the Chelsea Piers sports center in New York City, not far from their new Manhattan apartment. The actress is also keeping busy: She continues work on a new film she co-wrote, Molly, which follows the life of a single mother and her daughter.
Reporting by ELAINE ARADILLAS
For much more on why Tom and Katie’s marriage crumbled, the phone call that ended it all and what role Scientology will play in Suri’s life, pick up this week’s issue of PEOPLE, on newsstands everywhere Friday