  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.
