Deformations of Extremal Black Holes and the UV

TL;DR

This paper investigates how UV corrections affect deformations of extremal black holes in AdS, revealing that marginal modes are sensitive to UV physics and that positivity bounds influence horizon behavior, with implications for the weak gravity conjecture.

Contribution

It extends the analysis of horizon deformations to extremal charged AdS black holes, demonstrating UV sensitivity of marginal modes and connecting EFT corrections to positivity bounds and the weak gravity conjecture.

Findings

UV corrections lead to worse horizon behavior for marginal modes.

Explicit UV completions confirm EFT predictions.

Positivity bounds relate to the sign of EFT corrections.

Abstract

It has recently been noted that deformations of extremal AdS black holes in four and higher dimensions are generically non-smooth or singular on the horizon. Further, it was found that certain deformations of asymptotically flat extremal black holes are marginal, causing the nature of the horizon to be strongly sensitive to UV corrections -- in particular, Wilson coefficients associated with consistent UV completions generically lead to worse behaviour on the horizon. In this work, we extend the discussion of deformed horizons in the presence of UV corrections to extremal charged black holes in AdS, where we find a tower of marginal perturbations for different black hole masses. We argue that the apparent UV sensitivity of marginal modes is, in fact, a feature of the UV theory which is correctly reproduced by the EFT, and illustrate this with explicit UV completions confirming the validity of the EFT. We demonstrate that the same holds for a scalar-Maxwell EFT with known UV completion. In the gravitational case, the sign of EFT corrections to marginal perturbations is generally connected with the signs implied by positivity bounds, with UV completions generically leading to worse behaviour on the horizon. We conjecture that this result is more generic, and use this to derive more general positivity bounds motivated by the weak gravity conjecture, which we illustrate with further evidence.