A Variational Approach to the Derivation of Conserved Quantities in Perfect Fluid Spacetimes

In general relativity, conserved quantities of a gravitating system can be viewed in terms of a localized gravitational field embedded in a highly symmetric background field. Analogous to Gauss's Law in electromagnetism, to find the conserved quantities, surface flux integrals across a boundary and/or an asymptotic region are utilized. Using the variational techniques of Iyer & Wald, the general strategy of deriving these surface flux integrals will be briefly outlined. Applications of this technique to asymptotically perfect fluid spacetimes will also be discussed.