Abstract
We study scalar perturbations of the five-dimensional rotating black holes and find an exact solution giving exact description of the Hawking radiation. Mathematically, the full solution for this spin-zero field is expressed in terms of the prolate spheroidal wave function with complex parameters. By using the spheroidal joining factor, we write the corresponding boundary condition and greybody factors. We also check that the exact result reproduces the low frequency limit of the greybody factor and shows good agreement with the known numerical results.
Highlights
JHEP06(2019)041 on the brane [16]
We study scalar perturbations of the five-dimensional rotating black holes and find an exact solution giving exact description of the Hawking radiation
The solution to the angular Teukolsky equation for brane scalar fields in 5D (3.1) is given by a generalized spheroidal function, and the separation constant is determined in terms of the spin-weighted spheroidal eigenvalue sλml (±iaω) which reduces to a spheroidal eigenvalue for s = 0 case [18, 30], A = sλml (a)(±iaω) − a2ω2 − s(s + 1), (3.3)
Summary
We consider a scalar field in background of the 5D Myers-Perry black holes. The scalar field propagates on the four-dimensional brane and obeys the linear equation coupled to the background gravity. We begin our discussion with the introduction of a real scalar field φ(x) whose dynamics is governed by the Klein-Gordon equation, This scalar field φ propagates on the four-dimensional brane in the five-dimensional bulk formed by the Myers-Perry black hole [29] whose metric is expressed in the Boyer-Lindquist coordinates as ds2 = 1 − μdt2 + 2a sin θ μdtdφ − sin θ. The time-dependent part T (t) of the linear equation (2.6) is solved by the general solution,. Since this algebraic equation can become meaningful only for m = 0 and ω+ + ω− = 0, the constant f in (2.7) is given by zero and from (2.6) φ-dependence should disappear, Y (θ, φ) = S(θ) Let us consider another case of A+ = 0 or A− = 0.
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