Horizon thermalization of Kerr black hole through local instability

The validity of our already proposed conjecture -- {\it horizon creates a local instability which acts as the source of the quantum temperature of black hole} -- is being tested here for Kerr black hole. Earlier this has been explicitly shown for spherically symmetric static black hole (SSS BH). The more realistic situation like Kerr spacetime, being stationary and axisymmetric, is a non-trivial example to analyze. We show that for a chargeless massless particle, the near horizon radial motion in Kerr spacetime, like SSS BH, can be locally unstable. The radial contribution in the corresponding Hamiltonian is $\sim xp$ kind, where $p$ is the canonical momentum and $x$ is its conjugate position of particle. Finally we show that the horizon thermalization can be explained through this Hamiltonian when one dose a semi-classical analysis. It again confirms that near horizon instability is liable for its own temperature and moreover generalizes the validity of our conjectured mechanism for the black hole horizon thermalization.