## 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## Accelerated frames of reference

With the equivalence principle, Einstein postulated that any gravitational field was equivalent to an accelerated frame of reference. I’ve been looking at the mathematical framework of general relativity. In my last post, I began a consideration of accelerated frames of reference by introducing Rindler coordinates. In this post, I want to begin from a classical point of view and move on to deconstructing Rindler just a bit. You might recall that subject to a uniform acceleration in the x-direction, a point particle of mass would move like where I’ve included a position offset at...

Read More## Rindler coordinates

Almost invariably, when the topic of accelerated frames of reference arise in the context of relativity, Rindler coordinates are introduced. As a result, I’m going to follow the bandwagon and introduce Rindler coordinates, and then I’m going to deconstruct Rindler to demonstrate alternatives. To begin at the beginning, let’s consider an accelerated frame of reference in a pre-relativity context. An excellent choice is that of a rotating mass, possibly an orbiting mass, moving with uniform circular motion around a center at a fixed radius, and with an angular velocity, . In...

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