# Breitenlohner-Freedman bound in AdS coupled theory

In this review of the AdS/CFT correspondence in section 2.2.2 we are given the scalar field equations of a quantum field theory in AdS spacetime. The energy-momentum tensor is given by $$T_{\mu\nu}=2\partial_\mu\phi\partial_\nu\phi-g_{\mu\nu}\left[(\partial\phi)^2+m^2\phi^2\right]+\beta\left(g_{\mu\nu}\nabla^\rho\nabla_\rho-\nabla_\mu\nabla_\nu+R_{\mu\nu}\right)\phi^2$$

This energy-momentum tensor comes from a scalar field action with an extra term coulping the $$\phi^2$$ field with the scalar curvature($$\sqrt{-g}\beta R_{\mu\nu}g^{\mu\nu}\phi^2$$). From this we are given the total energy as $$E=\int{d^{p+1}x\sqrt{-g}T_0^0}$$ From here I'm not sure how we end up with the flux term $$\int_{S_p}{d\Omega_p\sqrt{g}n_iT^i_0}=0$$ and then $$(\tan\theta)^p\left[(1-2\beta)\partial_\theta+2\beta\tan\theta\right]\phi^2\rightarrow0$$