## Mr Schwarzschild meet Mr Rindler

In this post, I get to introduce Mr Schwarzschild to Mr Rindler thereby connecting a solution to Einstein’s field equations of general relativity, on the one hand, to an accelerated frame of reference, on the other. Along the way, we get to view the naked singularity within a black hole, at least mathematically, where it is less fatal. Mr Schwarzschild Recall from that previous post that the Schwarzschild metric in spherical coordinates is given by where is the Newton gravitational constant, is the mass at the origin of coordinates, is the distance from the origin, is the azimuthal...

Read More## Schwarzschild’s solution

Einstein published his general relativity in 1915; and in this, he included an approximate solution for the orbit of Mercury. At that time, Karl Schwarzschild had been deployed by the German army to the Russian front. Schwarzschild wrote Einstein with an exact solution to the field equations on December 22, 1915 (my oldest sister’s birthday, for whatever that’s worth). Schwarzschild used polar coordinates instead of the rectangular Cartesian coordinates that Einstein had originally employed; and this makes much more sense in any system with spherical symmetry, of course. I want...

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