I will consider the structure of arbitrary spacetimes with a finite null
boundary. The behaviour of the spacetime metric near the null boundary can be
described using Gaussian null coordinates. This description reveals the
universal structure on the boundary which is common to all spacetimes.
Diffeomorphisms which preserve the coordinate form of the metric, or
equivalently the universal structure, give rise to an infinite-dimensional
symmetry algebra on the null surface, analogous to the BMS symmetries at null
infinity. I show how the Wald-Zoupas prescription can be used to obtain the
charges and fluxes associated with these symmetries in general relativity. As an
example, we consider a causal diamond, and show that the symmetries imply
infinitely-many conservation laws between the past and future null boundaries of
a causal diamond in any spacetime satisfying the Einstein equation.