Can someone be held in a maximum security prison when they have no actual charges on them and they moved them to another state all cuz of someone lying on them, how long can they be held?

they can be held as long as the prison administration says. If another inmate is accusing you of something, both go to solitary confinement (the SHU) until the "investigation" is over. If they find nothing, they are stepped down back into gen pop, if not, they could spend a lot more time in max