where 2 n = ( l − − 1 ) ( l + 2 ) and l = 2 , 3 , 4 , … … characterizes the eigenmode for the θ θ coordinate. For gravitational perturbations, the modes l = 0 , 1 are irrelevant because they do not evolve with time. Physically gravitational perturbations with l = 0 (monopole) mode represents a change in the black hole mass, whereas the l = 1 (dipole) mode corresponds to a shift in the location and value of the black hole's angular momentum. The shape of above potentials are exhibited in the figure.