Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries

Understand

We provide a general formulation for calculating conserved charges for solutions to generally covariant gravitational theories with possibly other internal gauge symmetries, in any dimensions and with generic asymptotic behaviors.

• These solutions are generically specified by a number of exact (continuous, global) symmetries and some parameters.
• We define "parametric variations" as field perturbations generated by variations of the solution parameters.
• Employing the covariant phase space method, we establish that the set of these solutions (up to pure gauge transformations) form a phase space, the \emph{solution phase space}, and that the tangent space of this phase space includes the parametric variations.