Quantum corrections to tidal Love number for Schwarzschild black holes

TL;DR

This paper derives a quantum sum rule linking tidal Love numbers to graviton emission, computes quantum corrections for Schwarzschild black holes, and demonstrates these corrections are finite and nonzero, contrasting classical results.

Contribution

It introduces a quantum sum rule for tidal Love numbers and calculates finite quantum corrections for Schwarzschild black holes, which vanish classically.

Findings

Quantum sum rule relates tidal susceptibility to graviton emission

Finite nonzero quantum corrections to Love number for Schwarzschild black holes

Classical Love number for Schwarzschild black holes vanishes

Abstract

A sum rule for tidal Love number is derived from quantum field theory computations, which relates tidal susceptibility of a spinless body to transition rates of its single graviton emission processes. An analogous sum rule for electromagnetism is given as an example, which is substantiated by comparing to the solved problem of the hydrogen atom. Based on the semiclassical Hawking radiation spectrum, a finite nonvanishing value for quantum corrections to the Love number of Schwarzschild black holes in general relativity is computed using the sum rule, which is known to classically vanish.