The point r = 0 represents a curvature singularity and the point r d − − 1 = b is a coordinate singularity when b > 0 . To see this, we switch to the coordinate system ( v , r , x 1 , . . . , x d − − 2 ) where v = t + r ∗ ∗ ( r ) and r ∗ ∗ ( r ) is defined by the differential equation,