Virial identities across the spacetime

Virial-like identities obtained through Derrick’s scaling argument are powerful, multipurpose tools to study general relativistic models. Applications comprise establishing no-go/hair theorems and numerical accuracy tests. In the presence of a horizon (also known as a 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 being of particular interest. In this letter, by performing a radial coordinate transformation, we generalize Derrick’s scaling argument to compute virial identities across the whole nonasymptotically flat spacetimes. The developed method is applied to the entire Reissner-Nordstrom-de Sitter spacetime. A convenient gauge that trivializes the gravitational contribution to the identity between horizons is also found.