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Mathematical discipline which studies some properties of smooth manifolds, which allow to generalize calculus to beyond $\mathbb{R}^n$. General relativity is written in this language.
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Maximal analytic extension of Robinson-Bertotti geometry
I want to find a maximal analytic extension of the Robinson-Bertotti metric given by
$$ds^2 = - \lambda^2 dt^2 +Q^2 \frac{d\lambda^2}{\lambda^2}+Q^2d\Omega_{S^2}^2.$$
Where $Q$ is a constant charge an …
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Relative Acceleration in Schwarzschild coordinates
Place an observer in spacetime such that the feet of the observer touches the Schwarzschild radius and the head is $x$ meters away from the Schwarzschild radius.
I want to calculate the relative acce …