4. For the direction of the resultant force, refer to the figure below: Source: quora.com The angles can be solved as follows: {eq}\alpha = cos^{-1} \left( \frac {R_x}{R_F}\right)\\ \beta = cos^{-1} \left( \frac {R_y}{...
That is, at each point, the coordinate lines are mutually perpendicular and point in the same direction. However, in curvilinear coordinate systems, the angles between the axes can change from point-to-point. In curvilinear coordinate systems, the coordinate lines have curvature (i.e., they ...
Let C = R_{\mu \nu \alpha \beta }R^{\mu \nu \alpha \beta } denote the Kretschmann scalar. Then a calculation shows C = 48 m^2/r^6. Therefore C \circ \gamma (r) \rightarrow \infty as r \rightarrow 0. \square3 The Coordinate Singularity for Milne-Like Spacetimes Let I \...