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In this article, we study scalar wave perturbations of arbitrary frequency to the five-dimensional (5D) Schwarzschild-Tangherlini black hole (STBH) within general relativity. For the first time, we derive a closed formula for the 5D partial wave gravitational Raman scattering amplitude applicable to a broad class of boundary conditions, expressed in terms of the Nekrasov-Shatashvili (NS) function for the reduced confluent Heun problem. Furthermore, up to O ( G 2 ) we compute the dynamical ℓ = 0 , and the static ℓ = 1 , scalar tidal Love numbers of the STBH by matching an effective field theory description for a scalar wave scattering off the black hole, to our novel ultraviolet-NS solutions. The matched Love numbers do not vanish and present renormalization group running behavior.
Akhtar et al. (Sun,) studied this question.