Using MapleTM or MathematicaTM or a similar program calculate the Einstein field equations...

Using MapleTM or MathematicaTM or a similar program calculate the Einstein field equations for spherical coordinates assuming Tμv = 0 everywhere except possibly for r = 0, where the coordinate system is undefined. The most general spherical static metric corresponds to an interval given by

where r, θ, and φ correspond to the usual three-dimensional spherical coordinates. Solve these equations using an integration constant m to obtain the Schwarzchild solution for a point source of mass m. As you will discover, these coordinates have a singularity at r = 2m. Show that this is a coordinate singularity (a singularity determined by the choice of coordinates) rather than a physical singularity by examining the components of Riemann as r crosses 2m.