I don't think I'm going to invite my girlfriend to the concert
That's a bit shady? Why won't you invite her?
She was the first one to know about this concert, but I don't want to go with her.
You should invite your partner to an event they are interested in. It could hurt her feelings if you go without inviting her.
I don't care if she breaks up with me. I want to go to the concert so if I break up with her she won't be able to stop me.
Is the concert that big of a deal that you don't want to invite her? She obviously knows about it first, so she probably wants to go too. Going to the concert as a couple would be enjoyable because both of you would be able to enjoy the concert in real time.