This paper studies how a specific short-distance correction to gravity changes the way a non-rotating (Schwarzschild) black hole reacts to a static tidal field. In standard general relativity, the static tidal Love numbers of four-dimensional Schwarzschild black holes are zero. The authors add a parity-even cubic Weyl term to the action (a higher-curvature correction that can appear in effective field theory) and compute the resulting electric, static tidal response for every multipole number ℓ ≥ 2.

To do this they work directly with the metric (the gravitational field) and organize the angular dependence through L = ℓ(ℓ+1). They reduce the angular problem to exact radial actions and then simplify the three metric perturbation equations, by a perturbative order-reduction, into a constrained two-dimensional first-order system. Eliminating one field produces a single scalar equation whose homogeneous part is the same operator that governs static tides in general relativity. The cubic correction then acts as a source that can resonate with that operator.

Using a Frobenius expansion near the horizon and a Green-function analysis, the authors obtain a closed form for the gauge-invariant Zerilli–Moncrief logarithmic running coefficient: β_ZM_ℓ = ε_e · 7 L^2 (L−2)^2 (L−4)(L−6)/12, where ε_e parametrizes the small cubic coupling and L = ℓ(ℓ+1). The factor (L−6) explains why the quadrupole (ℓ = 2) is exceptional: it is the only electric multipole without logarithmic running. The paper also finds exact global metric solutions for ℓ = 2 (quadrupole) and ℓ = 3 (octupole). For the quadrupole they obtain a fixed-integer Zerilli–Moncrief branch ratio −2400 ε_e; this differs from the canonical analytically continued Love number k^E_2 = 448 ε_e because the two finite parts are defined in different ways.