This is sort of based on a scene recounted on the cast commentary of The Two Towers. Miranda Otto, who played Éowyn, recounted that when she first saw Liv Tyler (who played Arwen), she had decided not to go up to her right away since she didn't think it would be right to just mingle with one of the "big stars." Liv Tyler, on the other hand, ran right up to Miranda Otto the moment she saw her, gave her a huge hug and started gushing about how they could hang out. Yes, this was the right woman to play Arwen. When you're that warm a person, how can it fail to come across on-screen?
I own nothing.
There was, to the casual observer, no reason to assume commonality between them, between the Queen of Gondor and the Steward's wife. They really could not be more different, Elf and daughter of Men, dark and fair, old and young. The only thing they had in common was a love of the King, and in the latter that love had settled on sisterly rather than romantic. They had this one commonality, and surely that would spark friction, would it not?
Arwen did not see why it needed to. Frankly, she could not understand the perspective of those who said that she and Éowyn had nothing in common.
Éowyn was young by the reckoning of Men, but did not look so in Arwen's gaze. The young Lady of Rohan had labored long under the weight of the Shadow, as it invaded her home and blighted her life. Arwen knew, and bought this knowledge with great pain, that the weight of the Shadow aged a person, especially a child of Men, in ways that simple years could not. Éowyn was not young in her heart. Sometimes, looking at her, Arwen could see someone who was almost equal in years to herself.
They had both seen the goodness and the warmth in Estel, even when he went about with his true destiny hidden to onlookers' eyes. This caused Arwen no envy. She was not possessed of a heart inclined to envy, secure in her love's love for her. But as she loved Estel, she wished for others to love him as well, and if Éowyn could see him as someone she, whom life had taught her to be guarded with her affections, could love, even when he had first appeared to her as a ragged traveler in Elven gray, then her sight was clear and her heart a good one.
They were both alone here in Gondor, away from their homelands and their kin. Arwen know that she had a steadfast ally in her husband, but even with him, she felt isolated, and knew that Éowyn, a fair-haired foreigner with the love of her husband but separated from her kin, must have felt the same.
So one day, Arwen held out her hand.
"Please… I wish for a friend and a sister spirit, and I sense both in you."
For one moment, Éowyn of Rohan stared at her, her pale eyes flicking from her face to her hand, and back again. Though she now breathed the free air, though the Shadow was gone, she was still solemn and fierce, and wary at times, and not quick to accept the hand of friendship.
Then, her long white hand curled around Arwen's.
Arwen beamed, and Éowyn smiled hesitantly back.