## Equations

### Einstein's Field Equations

The formula results in a set of 16 equations, while 10 of them are independent (non-symmetric). Vividly spoken $T_{\mu \nu}$ prescribes the appearance of $R_{\mu \nu}$ which in turn prescribes a body's trajectory along a worldline.

### Relativistic Line Element

### Description for non-rotating Black Holes (Schwarzschild solution)

**Observer**: When a traveler is approaching the black hole's SSR $(r \rightarrow R_S)$ time elapses more and more slowly, while space bends and expands. When reaching $r = R_S$ time stands still and space becomes infinite. The traveler doesn't move anymore and appears infinitely red-shifted.

**Traveler**: When passing through the event horizon $(r < R_S)$ the algebraic signs of the first two terms inverse, thus causality and the dimensions of space $(3D \rightarrow 1D)$ and time $(1D \rightarrow 3D)$ turn. One has all the freedom moving through time, but is limited in space by only being able to move towards the singularity. Simultaneously, due to gravity, light falling into the black hole from the outside appears infinitely blue-shifted which results in a X-ray or Gamma-ray burst. The tidal forces become huge.

### Kerr-Newman metric

### Description for rotating Black Holes (Kerr solution)

### Kerr-Newman solution (with charge)

### Mass-Energy Equivalence

**approximation**, derived from the linearization of the Lorentz factor, only valid for $v << c$.

### Relativistic Time Dilation

An observer, moving with a constant speed $\textbf{v}$, a time $\textbf{t}$ in the observed rest frame will be dilated to $\textbf{t'}$.

If both, the observer and the observed system remain in their inertial system, they must be treated equally and it's not possible to distinguish who is moving or to whom the effect shall be applied. If the observer changes his state of movement, he leaves his related inertial system and so this effect will be attributed to him - even retrospectively.

### Relativistic Length Contraction

An observer, moving with a constant speed $\textbf{v}$ along a path $\textbf{l}$ in the observed rest frame, will see this path being shortened to $\textbf{l'}$. (Details: see obove.)

### Equation of Continuity

The density $\boldsymbol{\rho}$ of some quantity decreases over time in a certain volume if the divergence $\boldsymbol{\nabla}$ of the flux $\textbf{j}$ of that quantity is positive.

### SchrĂ¶dinger Equation

While investigating a particle as is there is no need to describe particles as waves with relation to circular motion ( $2\pi$). Thus $\boldsymbol{\hbar}$ is used to describe __ particles'__ quantum of action, not only if angular frequencies are used!

### Einstein's Deviation of Light in the Gravitational Field

### Gaussian Law

### Gaussian Law for Magnetism

### Faraday's Law of Induction

### AmpĂ©re's Circuital Law

### Light Speed in Vacuum

### Entropy Change

### Navier-Stokes Equation

Term 1: Intertial forces, Term 2: Pressure forces, Term 3: Viscous forces, Term 4: External forces

### General Momentum Balance

### Heat Transfer Equation (convective, diffusive)

### Poynting-Vector (Irradiance)

### Planck's Law of Radiation

### Einstein Coefficents

Because the spontaneous transitions dramatically increase with higher frequencies of light, it is cumbersome to construct a Short-Wavelength-LASER. The solution for this problem is to increase the intensity of the radiation field. In MRI-Technology the probability for induced effects is close to certainty.