Editing Nexus World (section)

== Advanced Mathematical Models of Nexus Forces ==

=== Nexus-Modified Maxwell Equations ===
The behavior of electromagnetic fields in Nexus Worlds is governed by modified Maxwell equations that include additional terms for Nexus influences:

<math>\nabla \cdot \mathbf{E} = \frac{\rho_{\text{charge}}}{\epsilon_0} + \sigma_{\text{Nexus}}</math>
<math>\nabla \times \mathbf{B} - \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t} = \mu_0 \mathbf{J} + \gamma_{\text{Nexus}} \mathbf{E}</math>
<math>\nabla \cdot \mathbf{B} = 0</math>
<math>\nabla \times \mathbf{E} + \frac{\partial \mathbf{B}}{\partial t} = 0</math>

Where:
* <math>\sigma_{\text{Nexus}}</math> and <math>\gamma_{\text{Nexus}}</math> are Nexus-specific field parameters.

These equations describe how electromagnetic fields are altered by the presence of Nexus Energy Fields, leading to unique phenomena such as altered light propagation, energy anomalies, and interdimensional field interactions.

=== Nexus Gravitational Waves ===
Nexus Worlds generate gravitational waves that propagate through higher dimensions, carrying energy and information across the multiverse. The equation governing these waves is a modified version of the standard gravitational wave equation:

<math>\Box h_{\mu\nu} + \Lambda_{\text{Nexus}} h_{\mu\nu} = \frac{16\pi G}{c^4} T_{\mu\nu}</math>

Where:
* <math>\Box</math> is the d'Alembertian operator.
* <math>h_{\mu\nu}</math> is the perturbation to the metric tensor representing the gravitational wave.
* <math>\Lambda_{\text{Nexus}}</math> is the Nexus-specific cosmological constant.
* <math>T_{\mu\nu}</math> is the energy-momentum tensor.

The term <math>\Lambda_{\text{Nexus}}</math> introduces modifications to the wave's behavior based on the Nexus Energy Field interactions, leading to potentially observable differences in wave patterns and energy dissipation.