Cutoffs, Stretched Horizons and Black Hole Radiators

Abstract

We argue that if the UV cutoff of an effective field theory with many low energy degrees if freedom is of the order, or below, the scale of the stretched horizon in a black hole background, which in turn is significantly lower than the Planck scale, the black hole radiance rate may not be enhanced by the emission of all the light IR modes. Instead, there may be additional suppressions hidden in the UV completion of the field theory, which really control which light modes can be emitted by the black hole. It could turn out that many degrees of freedom cannot be efficiently emitted by the black hole, and so the radiance rate may be much smaller than its estimate based on the counting of the light IR degrees of freedom. If we apply this argument to the RS2 brane world, it implies that the emission rates of the low energy CFT modes will be dramatically suppressed: its UV completion is given by the bulk gravity on $AdS_5 \times S^5$, and the only bulk modes that could be emitted by a black hole are the 4D s-waves of bulk modes with small 5D momentum, or equivalently, small 4D masses. Further, their emission is suppressed by bulk warping, which lowers the radiation rate much below the IR estimate, yielding a radiation flux $\sim (T_{BH} L)^2 {\cal L}_{hawking} \sim (T_{BH}/M_{Pl})^2 N {\cal L}_{hawking}$, where ${\cal L}_{hawking}$ is the Hawking radiation rate of a single light species. This follows directly from low CFT cutoff $\mu \sim L^{-1} \ll M_{Pl}$, a large number of modes $N \gg 1$ and the fact that 4D gravity in RS2 is induced, $M_{Pl}^2 \simeq N \mu^2$.