H G p h e n [ N ] = 1 16 π G ∫ Σ d 3 x N ¯ [ − 6 p ¯ ( sin μ ¯ γ k ¯ μ ¯ γ ) 2 − 1 2 p ¯ 3 / 2 ( sin μ ¯ γ k ¯ μ ¯ γ ) 2 ( δ E j c δ E k d δ c k δ d j ) + p ¯ ( δ K c j δ K d k δ k c δ j d ) − 2 p ¯ ( sin m μ ¯ γ k ¯ m μ ¯ γ ) ( δ E j c δ K c j ) + 1 p ¯ 3 / 2 ( δ c d δ j k δ e f ∂ e E j c ∂ f E k d ) ] ~ H_{\rm G}^{\rm phen}[N]=\frac{1}{16\pi G}\int_{\Sigma}\mathrm{d}^{3}x\bar{N}\left[-6\sqrt{\bar{p}}\left(\frac{\sin\bar{\mu}\gamma\bar{k}}{\bar{\mu}\gamma}\right)^{2}-\frac{1}{2\bar{p}^{3/2}}\left(\frac{\sin\bar{\mu}\gamma\bar{k}}{\bar{\mu}\gamma}\right)^{2}(\delta E^{c}_{j}\delta E^{d}_{k}\delta_{c}^{k}\delta_{d}^{j})+\sqrt{\bar{p}}(\delta K_{c}^{j}\delta K_{d}^{k}\delta^{c}_{k}\delta^{d}_{j})-\frac{2}{\sqrt{\bar{p}}}\left(\frac{\sin m\bar{\mu}\gamma\bar{k}}{m\bar{\mu}\gamma}\right)(\delta E^{c}_{j}\delta K_{c}^{j})+\frac{1}{\bar{p}^{3/2}}(\delta_{cd}\delta^{jk}\delta^{ef}\partial_{e}E^{c}_{j}\partial_{f}E^{d}_{k})\right]~{}