$S_{probe}=-\left(T_{4}L\right)\int d^{4}x\sqrt{-g}\left[\frac{1}{2}\left(1+\frac{g_s\pi \sin \theta }{2\left(M_{s}L\right){\left(M_{s}y\right)}^2}\right)|\partial y{|}^2-2\left(1-\frac{g_s\pi {\tan }^3\theta }{8\left(M_{s}L\right){\left(M_{s}y\right)}^2}\right)\right]$