Tidal Love numbers of static black holes in anti-de Sitter

TL;DR

This paper computes the tidal Love numbers for four-dimensional Schwarzschild black holes in global anti-de Sitter space, linking bulk gravitational perturbations to boundary plasma polarization, and compares different formalisms for the calculation.

Contribution

It extends the understanding of tidal Love numbers from black branes to Schwarzschild black holes in AdS, using multiple gauges and relating formalisms for holographic analysis.

Findings

Tidal Love numbers for Schwarzschild-AdS black holes are computed.

Results show agreement between different gauge-invariant formalisms.

Comparison with black brane results confirms consistency in the holographic framework.

Abstract

Tidal Love numbers of anti-de Sitter black holes are understood as linear response coefficients governing how the holographically dual plasma polarizes when the geometry of the space, in which the plasma lives, is deformed. So far, this picture has been applied only to black branes with plane wave perturbations. We fill the gap in the literature by performing the computation of tidal Love numbers for the four-dimensional Schwarzschild solution in global anti-de Sitter, which is dual to a conformal plasma on $S^2$. We conclude about the effect of the bulk gravitational perturbations on the boundary metric and stress tensor, responsible for the geometric polarization. The computation of the tidal Love numbers is performed in both Regge-Wheeler gauge and the Kodama-Ishibashi gauge-invariant approach. We spell out how to convert the tidal Love numbers determined in these two formalisms and find perfect agreement. We also relate the Kodama- Ishibashi formalism with the Kovtun-Starinets approach, which is particularly well suited for the holographic analysis of black branes. This allows us to compare with the tidal Love number results for black branes in anti-de Sitter, also finding agreement in the relevant regime.