User:GeodesicEFE

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

Linearized General Relativity with an Electromagnetic Field

$\partial _{\nu }F^{\mu \nu }=\mu _{0}j^{\mu }$

$\partial _{\sigma }F_{\mu \nu }+\partial _{\nu }F_{\sigma \mu }+\partial _{\mu }F_{\nu \sigma }=0$

${\bar {h}}_{\mu \nu }=h_{\mu \nu }-{\frac {1}{2}}\eta _{\mu \nu }h$

$\Box {\bar {h}}_{\mu \nu }={\frac {4\pi G}{\mu _{0}c^{4}}}\left(4\eta ^{\alpha \beta }F_{\mu \alpha }F_{\beta \nu }-\eta _{\mu \nu }\eta ^{\alpha \gamma }\eta ^{\beta \delta }F_{\beta \gamma }F_{\alpha \delta }\right)-{\frac {16\pi G}{c^{4}}}T_{\mu \nu }^{M}$

${\frac {d^{2}x^{\mu }}{d\tau ^{2}}}+{\frac {1}{2}}\eta ^{\mu \sigma }\left(\partial _{\beta }h_{\sigma \alpha }+\partial _{\alpha }h_{\sigma \beta }-\partial _{\sigma }h_{\alpha \beta }\right){\frac {dx^{\alpha }}{d\tau }}{\frac {dx^{\beta }}{d\tau }}={\frac {q}{m}}\left(\eta ^{\mu \sigma }-h^{\mu \sigma }\right)F_{\nu \sigma }{\frac {dx^{\nu }}{d\tau }}$