Question

need some questions... for my teachers.. cause.. "REVENGE IS SWEET"

Answer 1

Let \[(U,V,\theta, \phi)\] be Kruskal coordinates on the Kruskal manifold, where \[\large-UV=\left(\frac{r}{2m}-1\right)e^{r/2m},\hspace{1cm} t=2m\ln\left(\frac{-V}{U}\right)\]
and θ and ϕ are the usual polar angles. The metric is
\[\large ds^2=\frac{-32m^3}{r}e^{\frac{-r}{2m}}dUdV+r^2d\Omega^2\]
The killing vector is:
\[\xi=-U\partial_U+V\partial_V\]

express ξ in exterior Schwarzschild coordinates.