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.
Highlights
At sufficiently large scales, any finite-sized system can be considered as a point particle
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
Summary
Any finite-sized system can be considered as a point particle. Tidal Love numbers parametrize susceptibilities of the body under tidal influences [16,17], which are analogs of electric and magnetic susceptibilities in electromagnetism They have gained interest as tidal interactions and are expected to leave recognizable imprints on the waveforms of gravitational waves, which can be detected by groundbased interferometers such as LIGO [18,19,20,21,22,23]. This sum rule can be used to compute quantum corrections to the tidal Love number of SBHs by treating them as scalar particles [35]. Natural units ħ 1⁄4 c 1⁄4 1 will be used throughout the letter unless explicitly stated
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