The Einstein--Hilbert action, coupled to matter with Lagrangian density $\mathcal{L}_m$, is
\[
S = \frac{1}{2\kappa} \int_M R \sqrt{-g}\, \mathrm{d}^4x \;+\; \int_M \mathcal{L}_m \sqrt{-g}\, \mathrm{d}^4x,
\qquad \kappa = \frac{8\pi G}{c^4},
\]
where $R = g^{\mu\nu} R_{\mu\nu}$ is the Ricci scalar, $g = \det(g_{\mu\nu})$, and $R_{\mu\nu}$ is the Ricci tensor built from the Christoffel…
See More...
1 / 3
First
userId 1 is admin on this software