Charges, conserved quantities and fluxes in de Sitter spacetime

TL;DR

This paper explores how to define and understand conserved charges and fluxes in asymptotically de Sitter spacetimes, highlighting their dependence on gravitational flux and the conditions for charge conservation.

Contribution

It introduces a method to define holographic charges at infinity and Cauchy surfaces in de Sitter spacetime, analyzing their dependence on gravitational flux and surface choices.

Findings

Charges are independent of the choice of surface if no gravitational flux is present.

Net gravitational flux causes the charges to change between different surfaces.

The paper provides a framework for understanding fluxes and charges 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 $I_t$ as integrals over the intersection of timelike surfaces $C$ and the Cauchy surface $I_t$. In general, the charges $Q^t$ defined on the Cauchy surface $I_t$ 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 $C_1, C_2$ and two Cauchy surfaces then $\Delta Q^t(C_1, C_2) = Q^t(C_1)-Q^t(C_2)$ changes by the same amount.