BMS type symmetries at null-infinity and near horizon of non-extermal black holes

Understand

In this paper we consider a generally covariant theory of gravity, and extend the generalized off-shell ADT current such that it becomes conserved for field dependent (asymptotically) Killing vector field.

• Then we define the extended off-shell ADT current and the extended off-shell ADT charge.
• Consequently, we define the conserved charge perturbation by integrating from the extended off-shell ADT charge over a spacelike codimension two surface.
• Eventually, we use the presented formalism to find the conserved charge perturbation of an asymptotically flat spacetime.