Charges, conserved quantities, and fluxes in de Sitter spacetime

Abstract

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analog of holographic charges at future and past infinity and at other Cauchy surfaces It as integrals over the intersection of timelike surfaces C and the Cauchy surface It. In general, the charges Qt defined on the Cauchy surface It depend on C, but if gravitational flux is absent the charges are independent of C. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by C1, C2 and two Cauchy surfaces then ΔQt(C1,C2)=Qt(C1)-Qt(C2) changes by the same amount.