Does free will exist, mathematically, on the inside of black hole? Perhaps. In order to break the chains of determinism you may have to pass through a firewall of energy containing all the information making up the total history of the universe. There's still a chance that the region beyond that firewall is no more free than the rest, it is practically an entirely separate universe anyways, the boundaries between may be cosmically censored and only giving the illusion of possibility. There's only one way to find out.