Virial identities across the spacetime

TL;DR

This paper generalizes virial identities across entire non-asymptotically flat spacetimes, including cosmological horizons, using a radial coordinate transformation, and applies it to Reissner-Nordstrom-de Sitter spacetime.

Contribution

It introduces a method to compute virial identities across whole non-asymptotically flat spacetimes, including multiple horizons, expanding previous approaches limited to outside the event horizon.

Findings

Successfully applied to Reissner-Nordstrom-de Sitter spacetime

Developed a gauge simplifying gravitational contributions

Extended virial identities to include cosmological horizons

Abstract

Virial-like identities obtained through Derrick's scaling argument are powerful, multi-purpose tools to study general relativistic models. Applications comprise establishing no-go/hair theorems and numerical accuracy tests. In the presence of a horizon (\textit{aka} boundary), the spacetime can be divided into regions, each with its own identity. So far, such identities have only been computed in the region outside the event horizon; however, adding a positive cosmological constant endows an additional boundary (the cosmological horizon), with the region between the latter and the former of particular interest. In this letter, by performing a radial coordinate transformation, we generalise Derrick's scaling argument to compute virial identities \textit{across the whole} non-asymptotically flat spacetimes. The developed method is applied to the entire Reissner-Nordstrom-de Sitter spacetime. A convenient gauge that trivialises the gravitational contribution to the identity between horizons is also found.