English

Virial identities across the spacetime

General Relativity and Quantum Cosmology 2024-06-04 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2406.00112,
  title  = {Virial identities across the spacetime},
  author = {Alexandre M. Pombo and Lorenzo Pizzuti},
  journal= {arXiv preprint arXiv:2406.00112},
  year   = {2024}
}

Comments

9 pages, 1 Figure

R2 v1 2026-06-28T16:49:02.171Z