Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity

Understand

We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an $(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant.

• We assume that the Gauss-Bonnet coupling constant is non-negative.
• The quasi-local mass was recently defined by one of the authors as a counterpart of the Misner-Sharp quasi-local mass in general relativity.
• The quasi-local mass is found to be a quasi-local conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law.