Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

General Relativity

Einstein's theory of gravity, providing the framework for understanding the universe's large-scale structure and the effects of dark matter and energy.
📜

The statement of the theorem

General Relativity is formulated by varying the Einstein-Hilbert action SS with respect to the metric gμνg_{\mu\nu}. The action is:\nS=∫d4x−g[c16πGR+Lmatter]S = \int d^4x \sqrt{-g} \left[ \frac{c}{16\pi G} R + \mathcal{L}_{matter} \right]\nWhere RR is the Ricci scalar, and Lmatter\mathcal{L}_{matter} is the Lagrangian density of matter and fields. Varying SS yields the field equations:\nc16πG(Rμν−12Rgμν)+∂Lmatter∂gμν=0\frac{c}{16\pi G} (R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu}) + \frac{\partial \mathcal{L}_{matter}}{\partial g_{\mu\nu}} = 0