# Conformally Soft Theorem In Gravity

## TL;DR

This paper demonstrates a celestial analogue of Weinberg's soft graviton theorem, showing how conformally soft particles in celestial amplitudes obey special relations due to celestial sphere symmetries, differing from traditional soft theorems.

## Contribution

It introduces conformally soft factorization in celestial amplitudes for gravity and identifies it as the celestial counterpart of Weinberg's soft graviton theorem.

## Key findings

- Conformally soft particles obey special relations in celestial amplitudes.
- The conformally soft theorem is analogous to Weinberg's soft graviton theorem.
- Celestial sphere symmetries govern the behavior of conformally soft particles.

## Abstract

A central feature of scattering amplitudes in gravity or gauge theory is the existence of a variety of energetically soft theorems which put constraints on the amplitudes. Celestial amplitudes which are obtained from momentum-space amplitudes by a Mellin transform over the external particle energies cannot obey the usual energetically soft theorems. Instead, the symmetries of the celestial sphere imply that the scattering of conformally soft particles whose conformal weights under the 4D Lorentz group SL(2,C) are taken to zero obey special relations. Such conformally soft theorems have recently been found for gauge theory. Here, I show conformally soft factorization of celestial amplitudes for gravity and identify it as the celestial analogue of Weinberg's soft graviton theorem.