Exploration of Holographic Eigen-spectra of 4D Black Hole Horizons

We perform a high accuracy numerical analysis of the energy Eigen-systems that arise for the two dimensionally reduced holographic field theories of four dimensional black holes coupled to massless scalars. These dimensionally reduced theories couple to two dimensional black holes which share the identical thermodynamic spectrum of their four dimensional parents and in most cases are also non-singular. Using Finite Element Analysis with cubic Hermite interpolation we probe the holographic eigen-spectrum for several different four dimensional black holes including Kerr-Newman-AdS. The motivation stems from the long held intuition that quantum gravity of black hole horizons only cares about the s-wave. Our analysis thus far seems to corroborate this intuition since our results show an antipodal spectrum for higher orders beyond the s-wave of l and m.