consider have a metric
ds^2=f(r,t)dt^2+g(r,t)dr^2+k(r,t)dΩ^2
if g(r,t) =0, we have black hole?
any metric that has this condition, are black hole? or not this is first clue to determine black hole and we should check some other features!
solution of g(r,t)=0, may have some roots, for example...