I started a relationship with a girl a month ago - my first real

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I started a relationship with a girl a month ago - my first real relationship (though not hers). She's really nice to me, she always cares about my feelings, and she tells me she loves me a lot. I make sure to tell her that I love her as well, because I really do love her. I care about her a lot, and her happiness means the world to me. I feel safe with her, I feel loved and cared for in a way that I've never felt with anyone before.
But her and I don't really share many interests. We have the same values and the same personality, but we don't share any of the same hobbies, nor do we like discussing the same things. We can talk about our feelings very openly and honestly, there's no problem there, but there's not much beyond that. We can't be together physically most of the time, so all we can do is Skype or talk over the phone, which means that all we have is our conversations. They usually result in silence. Neither of us minds the silence much, but I'm afraid that someday I will care, that I'll get sick of it and will start to crave some deep conversation. That's what scares me, I don't want to get too invested into her and then realized that things won't work out, and more than that I don't want to waste her time.
I'm also afraid that I'm going to be missing out because of this. I've never had a girlfriend before her, and I'm afraid I'll miss out on perhaps having a partner that I have genuine and interesting conversations. But I'm also afraid that I'd be making a big mistake if I broke up with her. Because like I said, I care a hell of a lot about her, and she's so sweet and kind to me - and I know that's not something you can find easily in this world. I don't want to lose such a great and terrific person over something that could be so petty.