User:GeodesicEFE

G'day it should be apparent from this page that I do adore elegant equations

Linearized General Relativity with an Electromagnetic Field
$$\partial_{\nu} F^{\mu\nu} =\mu_{0} j^{\mu} $$ $$ \partial_{\sigma} F_{\mu\nu}+\partial_{\nu} F_{\sigma\mu}+\partial_{\mu} F_{\nu\sigma}=0 $$ $$ \bar{h}_{\mu\nu}=h_{\mu\nu} -\frac{1}{2} \eta_{\mu\nu} h $$ $$ \Box \bar{h}_{\mu \nu} = \frac{4 \pi G}{\mu_{0} c^4} \left(4 \eta^{\alpha\beta} F_{\mu\alpha} F_{\beta\nu}-\eta_{\mu\nu} \eta^{\alpha\gamma} \eta^{\beta\delta} F_{\beta\gamma} F_{\alpha\delta}\right)-\frac{16\pi G}{c^{4}} T^M_{\mu\nu}$$ $$ \frac{d^{2} x^{\mu}}{d\tau^{2}}+\frac{1}{2} \eta^{\mu\sigma} \left(\partial_{\beta} h_{\sigma\alpha} +\partial_{\alpha} h_{\sigma\beta}-\partial_{\sigma} h_{\alpha\beta}\right) \frac{d x^{\alpha}}{d\tau} \frac{d x^{\beta}}{d\tau}=\frac{q}{m} \left(\eta^{\mu\sigma}-h^{\mu\sigma}\right) F_{\nu\sigma} \frac{d x^{\nu}}{d\tau} $$