Is Mr Rochester in Jane Eyre?

The main arc of the Rochester part of the book is like he and Antoinette are kind of okay. They have a good like physical relationship for a while but then somebody who claims to be Antoinette's like half brother starts to send him mail talking about how untrustworthy she is. The impression that we get in this book is Mr. Rochester does sure does need money, his father and older brother do seem to be like a bit of a burden on him. He doesn't care at all for Jamaica like he is he is pining constantly for the gray rainy city streets of England I saw.