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 analogue 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 Q t defined on the Cauchy surface It depend on C, but their difference ∆Q t (C1, C2) = Q t (C1) − Q t (C2) is a conserved quantity under time evolution (i.e. independent of the Cauchy surface) if gravitational flux is absent. 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 ∆Q t (C1, C2) changes by the same amount.