Continuous area spectrum of a regular black hole

We investigate highly damped quasinormal modes of regular black hole coupled to nonlinear electrodynamics. Using the WKB approximation combined with complex-integration technique, we show that the real part of the frequency disappears in the highly damped limit. If we use the Bohr’s correspondence principle, the area spectrum of this black hole is continuous. We discuss its implications for loop quantum gravity.

Figure 1

A schematic illustration of the Stokes (dashed lines) and anti-Stokes (solid lines) for the regular black hole problem in the complex $r$-plane in the limit $\mathrm{Im}(\omega )\to -\infty$. The open and filled circles represent zeros and poles of $Q^2(r)$, respectively.