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

TL;DR

This paper argues that certain residual diffeomorphisms in general relativity, called symplectic symmetries, can distinguish physically different geometries, leading to the concept of symplectic soft hair on black holes that may address the microstate problem.

Contribution

It introduces the idea of residual diffeomorphisms as symplectic symmetries and proposes their role as black hole soft hair, refining the strict equivalence principle in GR.

Findings

Residual diffeomorphisms can be associated with conserved charges.

Symplectic symmetries are a general feature beyond specific examples.

Black hole geometries may possess symplectic soft hair as horizon microstates.

Abstract

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".