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

Residual Diffeomorphisms and Symplectic Softs Hairs: The Need to Refine Strict Statement of Equivalence Principle