  General covariance is the cornerstone of Einstein's General Relativity (GR)
and implies that any two metrics related by diffeomorphisms are physically
equivalent. There are, however, many examples pointing to the fact that this
strict statement of general covariance needs refinement. There are a very
special (measure-zero) subset of diffeomorphisms, the residual diffeomrphisms,
to which one can associate well-defined conserved charges. This would hence
render these diffeomorphic geometries physically distinct. We discuss that
these symmetries may be appropriately called "symplectic symmetries". Existence
of residual diffeomorphisms and sympelctic symmetries can be a quite general
feature and not limited to the examples discussed so far in the literature. We
propose that, in the context of black holes, these diffeomorphic, but distinct,
geometries may be viewed as "symplectic soft hair" on black holes. We comment
on how this may remedy black hole microstate problem, which in this context are
dubbed as "horizon fluffs".
