Editing Electrogravitics (section)

==== Stress-Energy Tensor ====
The stress-energy tensor, denoted by <math>T^{\mu\nu}</math>, plays a central role in describing the distribution of energy and momentum in spacetime. In the context of electromagnetism and gravity, the stress-energy tensor incorporates contributions from electromagnetic fields, matter, and gravitational effects. The equations governing the stress-energy tensor include:

  <math>T^{\mu\nu} = \frac{1}{\mu_0} \left( F^{\mu\lambda} F^\nu{}_\lambda - \frac{1}{4} g^{\mu\nu} F_{\alpha\beta} F^{\alpha\beta} \right) + T^{\mu\nu}_{\text{matter}}</math>

* <math>T^{\mu\nu}</math>: Stress-energy tensor representing the energy-momentum distribution in spacetime.
* <math>F^{\mu\lambda}</math>: Electromagnetic field tensor.
* <math>g^{\mu\nu}</math>: Metric tensor representing the spacetime metric.
* <math>\mu_0</math>: Vacuum permeability constant.
* <math>T^{\mu\nu}_{\text{matter}}</math>: Stress-energy tensor of matter, including contributions from mass and energy.

  <math> T^{\mu\nu} = \varepsilon_0 \left( E^\mu E^\nu - \frac{1}{2} g^{\mu\nu} E_\alpha E^\alpha \right) + \frac{1}{\mu_0} \left( B^\mu B^\nu - \frac{1}{2} g^{\mu\nu} B_\alpha B^\alpha \right) - \frac{1}{4\pi} \left( R^{\mu\nu} - \frac{1}{2} g^{\mu\nu} R \right) </math>

* <math>\varepsilon_0</math>: Vacuum permittivity constant.
* <math>E^\mu</math>: Electric field components.
* <math>B^\mu</math>: Magnetic field components.
* <math>R^{\mu\nu}</math>: Ricci curvature tensor representing the curvature of spacetime.
* <math>R</math>: Ricci scalar representing the scalar curvature of spacetime.