Perturbations and absorption cross-section of infinite-radius black rings

Abstract

We study scalar field perturbations on the background of non-supersymmetric black rings and of supersymmetric black rings. In the infinite-radius limit of these geometries, we are able to separate the wave equation, and to study wave phenomena in its vicinities. In this limit, we show that (i) both geometries are stable against scalar field perturbations, (ii) the absorption cross-section for scalar fields is equal to the area of the event horizon in the supersymmetric case, and proportional to it in the non-supersymmetric situation.

Figures (3)

• Figure 1: The real part of the fundamental mode ($n=0$) of $l=0$ perturbations, as a function of the boost parameter $\sigma$. Here we show the characteristic frequencies for several values of $k$. For small values of $\sigma$ and $k$, the real part of the frequency yields ${\rm Re}(\omega) \sim 0.22$, which is the Schwarzschild value.
• Figure 2: The imaginary part of the fundamental mode ($n=0$) of $l=0$ perturbations, as a function of the boost parameter $\sigma$. For small values of $\sigma$ and $k$, the imaginary part of the frequency yields ${\rm Im}(\omega) \sim 0.21$, which is the Schwarzschild value.
• Figure 3: The same as Figs \ref{['fig:f1']} and \ref{['fig:f2']}, but for $l=1$.