# Gapless Topological Order, Gravity, and Black Holes

## TL;DR

This paper shows that linearized gravity has gapless topological order with many ground states, linking it to black hole physics, soft theorems, and topological sectors, offering new insights into quantum gravity and information paradoxes.

## Contribution

It demonstrates that linearized gravity exhibits gapless topological order with extensive ground state degeneracy, connecting soft theorems to topological sectors and black hole phenomena.

## Key findings

- Linearized gravity has extensive ground state degeneracy.
- Topological sectors correspond to symmetries described by Hawking et al.
- Black holes can be viewed as topological defects in the IR theory.

## Abstract

In this work we demonstrate that linearized gravity exhibits gapless topological order with an extensive ground state degeneracy. This phenomenon is closely related both to the topological order of the pyrochlore U(1) spin liquid and to recent work by Hawking et. al. who used the soft photon and graviton theorems to demonstrate that the vacuum in linearized gravity is not unique. We first consider lattice models whose low-energy behavior are described by electromagnetism and linearized gravity, and then argue that the topological nature of these models carries over into the continuum. We demonstrate that these models can have many ground states without making assumptions about the topology of spacetime or about the high-energy nature of the theory, and show that the infinite family of symmetries described by Hawking et. al. are simply the difierent topological sectors. We argue that in this context black holes appear as topological defects in the IR theory, and that this suggests a potential approach to understanding both the firewall paradox and information encoding in gravitational theories. Finally, we use insights from the soft boson theorems to make connections between deconfined gauge theories with continuous gauge groups and gapless topological order.