The AdS4 Gravitational Perturbation and Supersymmetry

Gravitational perturbation in AdS(4), decomposed into axial and polar perturbations that have different parities. After imposing geometric perturbation in to the spherical, symmetric and static metric of AdS(4), we can calculate the possible spectrum of frequencies around the static configuration. This spectrum relates to the boundary conditions imposed at spatial infinity (r = infinity) and will be implied by the wave function's behavior at x = pi/2 or y = 1. At the end we write down the first order raising and lowering operators from the second order Schrodinger equation to study the supersymmetry model and check whether we have supersymmetric partners or no. After finding the H-1 and the partner H-2, we check the supersymmetry. At the end, we find the potentials to confirm the shape invariance condition and also the supercharges and their commutative relations are studied.