They also changed his shooting schedule after this shot to add him to some of the scenes where Eowyn was in the House of Healing. They’d expected something more downplayed - shocked, and upset, but fairly stoic, like a stereotypical fantasy hero man - but they said when they saw this display of emotion, they couldn’t imagine him not being there watching over her heal.
One thing that really makes me mad about the movies is that half of the best speeches are stolen from Eomer in the books. Théoden’s warcry of “Death!” at the Battle of the Pelennor Fields was actually made by Eomer after he found out that Théoden had died and he was now in command. He was also smart and charming, but overall the Eomer of the books was emotional and very much listened to his heart over anything else.
Karl Urban is a phenomenal actor, and I really feel like he understood the character of Eomer as he was represented in the books. And I love that.