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arxiv: 2406.00112 · v1 · pith:W33U2UWXnew · submitted 2024-05-31 · 🌀 gr-qc · math-ph· math.MP

Virial identities across the spacetime

classification 🌀 gr-qc math-phmath.MP
keywords identitieshorizonspacetimeacrossargumentboundarycosmologicalderrick
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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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