A convenient gauge for virial identities in axial symmetry

Virial identities are a useful mathematical tool in General Relativity. Not only have they been used as numerical accuracy tool, but also played significant role establishing no-go and no-hair theorems while giving some physical insight into the considered system from an energy balance perspective. While calculation of these tends to be straightforward application Derrick's scaling argument [1], complexity resulting identity is dependent. In particular, contribution Einstein-Hilbert action, due presence second order derivatives metric functions, becomes increasingly complex for generic metrics. Additionally, Gibbons-Hawking-York term needs taken account [2]. Thankfully, since gravitational action depends on metric, it expected that “convenient” gauge trivializes exists. spherical symmetry such known (the m−σ parametrization), has not found axial symmetry. this letter, we propose use compute Kerr black holes with scalar hair.