ag-gipp/GoUldI

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]