How to prove $-\ln(1-\|x\|^2)$ is self-concordant function?

Question

I'm trying to prove $-\ln(1-\|x\|^2_2)$ is self-concordant function.

I think 1-dim case is easy to prove, but I cannot prove multi-dim cases. It's really hard to use definition because heavy Hessian. Can anyone help me with that? Thank you!