Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that “coordinates matter” using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the Landau-Lifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems.
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Our title paraphrases a famous political dictum. During Bill Clinton's first campaign for the U.S. presidency, his top advisor James Carville tried to keep him focused on talking about the previous administration's economic failures by repeatedly telling him: “It's the economy, stupid!”
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© 2014 American Association of Physics Teachers.
2014
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