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Question: Maple Problem From Goldstein, Poole, and Safko's "Classical Mechanics"

Question:Maple Problem From Goldstein, Poole, and Safko's "Classical Mechanics"

dcasimir 1212
January 28 2008
0
This problem (problem # 30) from Goldstein's "Classical Mechanics" specifically asks one to use Maple. The problem is as follows. Using Maple or Mathematica or a similar program calculate the Einstein field equations for spherical coordinates assuming T[mu,nu] = 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 (ds)^2 =e^(nu(r))*(c^2)*(dt)^2 - e^(lambda(r))*(dr^2) - r^2*((dtheta^2) + sin^2(theta)*(dphi^2)), where r, theta, and phi 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. Please Help, anyone (John Fredsted this sounds like one of your favorites very respectfully, dc
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