Black hole stereotyping: Induced gravito-static polarization

TL;DR

This paper calculates the gravito-static polarization constants of black holes across different dimensions, revealing they vanish in 4D but are non-zero in higher dimensions, challenging previous assumptions.

Contribution

It provides the first comprehensive calculation of black hole Love numbers in arbitrary dimensions, clarifying their behavior and implications for black hole effective couplings.

Findings

In 4D, black hole Love numbers vanish, confirming previous results.

In higher dimensions, Love numbers are non-zero, indicating effective couplings beyond point particles.

Certain Love numbers exhibit a classical renormalization flow and can be negative, suggesting instabilities.

Abstract

We discuss the black hole effective action and define its static subsector. We determine the induced gravito-static polarization constants (electric Love numbers) of static black holes (Schwarzschild) in an arbitrary dimension, namely the induced mass multipole as a result of an external gravitational field. We demonstrate that in 4d these constants vanish thereby settling a disagreement in the literature. Yet in higher dimensions these constants are non-vanishing, thereby disproving (at least in d>4) speculations that black holes have no effective couplings beyond the point particle action. In particular, when l/(d-3) is half integral these constants demonstrate a (classical) renormalization flow consistent with the divergences of the effective field theory. In some other cases the constants are negative indicating a novel non-spherical instability. The theory of hypergeometric functions plays a central role.