S p r o b e = − ( T 4 L ) ∫ d 4 x − g [ 1 2 ( 1 + g s π sin θ 2 ( M s L ) ( M s y ) 2 ) | ∂ y | 2 − 2 ( 1 − g s π tan 3 θ 8 ( M s L ) ( M s y ) 2 ) ] S_{\rm probe}=-(T_{4}L)\int d^{4}x\,\sqrt{-g}\left[{1\over 2}\left(1+\frac{g_{s}\pi\sin\theta}{2(M_{s}L)(M_{s}y)^{2}}\right)|\partial y|^{2}-2\left(1-\frac{g_{s}\pi\tan^{3}\theta}{8(M_{s}L)(M_{s}y)^{2}}\right)\right]