Greybody Factors for d-Dimensional Black Holes

Abstract

Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically de Sitter and anti-de Sitter (Ads) spacetimes is provided). This calculation includes both the low-energy case -where the frequency of the scattered wave is small and real -and the asymptotic case -where the frequency of the scattered wave is very large along the imaginary axis -addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically de Sitter black holes the greybody e-print archive: http://lanl.arXiv.org/abs/0708.0017 TROELS HARMARK, JOSÉ NATÁRIO AND RICARDO SCHIAPPAfactor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically Ads black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure Ads spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically de Sitter black holes the greybody factors are given by non-trivial functions, while for asymptotically Ads black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).

Greybody factors for scalar fields emitted by a higher-dimensional Schwarzschild–de Sitter black hole

“…However, the analytical study was limited to the case of the lowest partial mode and in the very low-energy regime, since the presence of the cosmological constant increases the complexity of the field equations and makes the analytic treatment particularly difficult. A later work [34] extended the analysis by computing the next-to-leading-order term in the expansion of the greybody factor in terms of the energy of the scalar particle, focusing again on the lowest partial mode. More recently, an analysis [35] restricted in the 4-dimensional case produced results for the greybody factor for arbitrary scalar partial modes.…”

A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild–anti de Sitter black holes

“…QNM frequencies can also be considered as the poles in black hole greybody factors which are important in the study of Hawking radiation. The analytical monodromy techniques which were developed by Motl and Neitzke in [3,4] to calculate the highly damped QNM frequencies of black holes are used by Neitzke [5] and Harmark et al [6] to compute the asymptotic greybody factors for static, spherically symmetric black holes. The QNMs of black holes may also shed some light on the quantum nature of gravity via Bohr's correspondence principal.…”

Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results

“…Due to the mathematical complexity of the mode equation, this seldom happens. Thus only in certain cases, such as the low frequency limit [2][3][4][5][6][7][8] or when the effective potential vanishes and propagation is trivial (Γ = 1), have analytic expressions for the gray-body factor previously been obtained.…”