Editing Nexus World (section)

== Advanced Spacetime Dynamics ==

=== The Nexus Metric ===
The unique geometry of [[spacetime]] within Nexus Worlds is characterized by a distinct metric that accounts for the multidimensional connections and the influence of [[Nexus Energy Fields]]. The Nexus Metric can be expressed as an extension of the [[Einstein Field Equations]], incorporating additional terms for interdimensional interactions.

<math>ds^2 = -\left(1 - \frac{2GM}{r} + \frac{\beta N_{\text{Nexus}}}{r^n} \right)dt^2 + \left(1 - \frac{2GM}{r} + \frac{\beta N_{\text{Nexus}}}{r^n} \right)^{-1}dr^2 + r^2 d\Omega^2</math>

Where:
* <math>ds^2</math> is the line element representing the spacetime interval.
* <math>G</math> is the gravitational constant.
* <math>M</math> is the mass of the object.
* <math>r</math> is the radial coordinate.
* <math>\beta N_{\text{Nexus}}</math> is the Nexus-specific energy term.
* <math>n</math> is a dimensional parameter related to the influence of higher dimensions.

This equation modifies the standard Schwarzschild metric by including the term <math>\frac{\beta N_{\text{Nexus}}}{r^n}</math>, which accounts for the influence of Nexus Energy Fields on the curvature of spacetime. This term becomes significant near Nexus Points, where interdimensional forces are strongest.

=== Multidimensional Gravitational Interactions ===
In Nexus Worlds, gravity is not confined to three dimensions but extends into higher-dimensional spaces (often referred to as "branes"). The gravitational interaction can be modeled using a generalized form of Newton's law, incorporating extra dimensions:

<math>F_{\text{Nexus}} = G \frac{m_1 m_2}{r^{2+n}} \left(1 + \frac{\kappa}{r^3}\right)</math>

Where:
* <math>F_{\text{Nexus}}</math> is the gravitational force between two masses.
* <math>n</math> is the number of additional dimensions.
* <math>\kappa</math> is the coupling constant that accounts for Nexus Energy influences.

This equation suggests that gravity weakens less rapidly with distance in the presence of additional dimensions, which is why Nexus Worlds, despite their distance, have profound effects on one another.