# Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity

## TL;DR

This paper derives new positivity bounds for scattering amplitudes involving gravity, providing an S-matrix proof of the weak gravity conjecture and implications for black hole stability and modified gravity theories.

## Contribution

It introduces novel positivity bounds applicable to theories with massless gravitons, linking amplitude constraints to black hole properties and the weak gravity conjecture.

## Key findings

- Extremal black holes are self-repulsive and unstable to decay.
- Provides an S-matrix proof of the weak gravity conjecture.
- Bounds apply to effective field theories of axions, $P(X)$ theories, and curved spacetimes.

## Abstract

We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, $M/|Q|<1$ in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of axions, $P(X)$ theories, weakly broken galileons, and curved spacetimes.