Quantum Probe of Ho\v{r}ava-Lifshitz Gravity

Abstract

Particle probe analysis of the Kehagias - Sfetsos black hole spacetime of Ho% \v{r}ava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The timelike naked singularity that develops when $\omega M^{2}<1/2$, is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. Quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint and thus, the naked singularity in the Kehagias - Sfetsos spacetime become quantum mechanically non - singular.