Positive energy and stability of black holes

Hollands and Wald showed that dynamic stability of stationary axisymmetric black holes is equivalent to positivity of canonical energy on a space of linearised axisymmetric perturbations satisfying certain boundary and gauge conditions. We show that the ``kinetic energy'' --- the energy of the perturbations that are odd under reflection in \( t \) and \(\phi \) --- is positive. We discuss implications of having a positive kinetic energy for proving exponential growth in the case where the ``potential energy'' can be made negative.