Hawking radiation from a (4+n)-dimensional black hole: exact results for the Schwarzschild phase
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We start our analysis by deriving a master equation that describes the motion of a field with arbitrary spin s on a 3-brane embedded in a non-rotating, uncharged (4+n)-dimensional black hole background. By numerical analysis, we derive exact results for the greybody factors and emission rates for scalars, fermions and gauge bosons emitted directly on the brane, for all energy regimes and for an arbitrary number n of extra dimensions. The relative emissivities on the brane for different types of particles are computed and their dependence on the dimensionality of spacetime is demonstrated — we therefore conclude that both the amount and the type of radiation emitted can be used for the determination of n if the Hawking radiation from these black holes is observed. The emission of scalar modes in the bulk from the same black holes is also studied and the relative bulk-to-brane energy emissivity is accurately computed. We demonstrate that this quantity varies considerably with n but always remains smaller than unity — this provides firm support to earlier arguments made by Emparan, Horowitz and Myers.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ad82cbbf1bf063002fd6808c1b1c8336c90faadb
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- BlackHawk: a public code for calculating the Hawking evaporation spectra of any black hole distribution (2019, background): “quation if the spherical wave is decomposed into spin weighted spherical harmonics Ssl(θ) and a radial component Rs(r). The radial component of the master equation is, for massless particles of spin s[18]: 1 ∆s d dr ∆s+1 dRs dr ! + K2 +is(2r− r H)K ∆ − 4isEr− λsl ! Rs = 0, (2.19) where ∆(r) ≡ r2h(r)”