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The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M G/c^2$.
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More precisely, Ω \Omega is invariant under any O ( μ ) O(\mu) gauge displacement ξ α \xi^{\alpha} satisfying ( ∂ t + Ω ∂ φ ) ξ α = 0 (\partial_{t}+\Omega\partial_{\varphi})\xi^{\alpha}=0 as well as ξ θ = 0 \xi^{\theta}=0 along the orbit; see Ref. [ 8 ]
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