Virial identities across the spacetime

Alexandre M. Pombo; Lorenzo Pizzuti

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arXiv · 2406.00112

Virial identities across the spacetime

Alexandre M. Pombo·Lorenzo Pizzuti

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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.

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Alexandre M. Pombo, Lorenzo Pizzuti. 2024-05-31. Virial identities across the spacetime. https://arxiv.org/abs/2406.00112

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