5-Dimensional Gravitational Raman Scattering: Scalar Wave Perturbations in Schwarzschild-Tangherlini Spacetime

TL;DR

This paper derives a formula for scalar wave Raman scattering in 5D Schwarzschild-Tangherlini black holes, computes scalar tidal Love numbers, and reveals their non-vanishing and renormalization group behavior.

Contribution

It introduces a novel closed-form scattering amplitude formula using the Nekrasov-Shatashvili function and computes scalar Love numbers up to second order in G.

Findings

Derived a closed formula for 5D Raman scattering amplitude.

Computed non-zero scalar tidal Love numbers with RG running.

Matched effective field theory with ultraviolet-NS solutions.

Abstract

In this Letter, we study scalar wave perturbations of arbitrary frequency to the 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 $\ell=0$, and the static $\ell=1$, 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.