Four-dimensional greybody factors and the effective string

TL;DR

This paper extends the effective string description of Hawking radiation from five-dimensional three-charge black holes to four-dimensional four-charge black holes by analyzing an M-theory brane intersection that yields a four-charge black hole upon compactification. The authors perform a semiclassical gravity calculation of greybody factors for KK-charged scalars, solving the radial equation via matched asymptotics and a hypergeometric inner region, and derive a universal absorption cross section in terms of the left- and right-moving temperatures $T_L$ and $T_R$ and the Hawking temperature $T_H$. They then show that the charged emission rate $\Gamma(\vec{k})$ matches precisely the prediction of the effective string with length $L_{eff}= n_1 n_2 n_3 L_1$ and central charge $c=6$, providing a nontrivial consistency check between gravity and the effective-string picture in four dimensions. Overall, the results bolster the view that certain four-dimensional black holes admit an effective string description, mirroring the established five-dimensional case and connecting M-theory brane intersections to black hole thermodynamics through concrete, testable formulas.

Abstract

Recently Maldacena and Strominger found that the calculation of greybody factors for $D=5$ black holes carrying three U(1) charges gives striking new evidence for their description as multiply wound effective strings. Here we show that a similar result holds for $D=4$ black holes with four $U(1)$ charges. In this case the effective string may be thought of as the triple intersection of the 5-branes in M-theory compactified on $T^7$.