Vanishing Love of Black Holes in General Relativity: From Spacetime Conformal Symmetry of a Two-dimensional Reduced Geometry

Understand

We study the underlying structure of the vanishing of the Love numbers of both Schwarzschild and Kerr black holes in terms of spacetime conformal symmetry in a unified manner for the static spin-$s$ fields.

• The perturbations can be reduced with the harmonic decomposition to a set of infinite static scalar fields in a two-dimensional anti-de Sitter spacetime~$({\rm AdS}_2)$.
• In the reduced system, each scalar field is paired with another, implying that all multipole modes of the perturbation can be regarded as symmetric partners, which can be understood from the property of the supersymmetry algebra.
• The generator of the supersymmetric structure is constructed from a closed conformal Killing vector field of ${\rm AdS}_2$.