I am now reading this attached paper. But i can not get energy result(2.8), and I calculated it and found it is zero. here is my process: firstly, i use Gauss law and rewrite the (2.6): ##E=\frac{1}{8 \pi} \iint \chi_{0}^{0 \beta} \mu_{\beta} d S##

where µβ is the outward unit normal vector over an inﬁnitesimal surface element dS,For a surface given by parametric equations x = rsinθcosφ, y = rsinθsinφ, z = rcosθ (where r is constant) one has µβ = {x/r, y/r, z/r} and dS = r^2sinθdθdφ

and the author get only one component:

##\chi_{0}^{01}=\frac{2 M}{r}(r-\alpha) \sin \theta##and I let β=0 and have:

##E=\frac{1}{8 \pi} \int_{0}^{2 \pi} \int_{0}^{\pi} \frac{2 M}{r}(r-\alpha) \sin \theta \frac{r \sin \theta \cos \varphi}{r} r^{2} \sin \theta d \theta d \varphi##

finally, I factor out all term that have nothing to do with θ,φθ,φ and get the integral:

##E=r^{2} \frac{2 M}{r}(r-\alpha) \frac{1}{8 \pi} \int_{0}^{2 \pi} \int_{0}^{\pi} \sin ^{3} \theta \cos \varphi d \theta d \varphi=\mathrm{o} ! ! !##!!!

which shows the zero, i want to know what is wrong, could you help me.