Equations in 3 D and a surface

I have made two 3D drawings ,   one representing the Einstein field equations of General Relativity and the other for the Dirac equation . The drawings were made using MathType , Photoshop , Illustrator and Mathematica . The Dirac and Einstein equations are two of the most important equations of advanced physics of the twentieth century.

I have already inserted a less complex drawing of the Einstein equations in the slideshow for the books page .

Here is the drawing for the Einstein field equations:

GReq03nf

I tried to represent at the bottom  the curvature of space-time by a massive object (the sphere or spherical body in the middle of the picture).

The equation at the top is the geodesic equation of motion in General Relativity.

I have studied General Relativity and Tensor Calculus in the past and I’m going to describe some elements of the equations in the two drawings . For more details one can refer to books , courses and works about advanced physics and about  these subjects .

In the geodesic equation of motion , the Christoffel symbols of the second kind are related to the Christoffel symbols of the first kind [ρσ,ν] and are given by

Christoffel-def

I think the field equations of General Relativity are the most important physics equations elaborated by Einstein . These equations were part of a successful attempt to unify Gravity and electromagnetism . They contain within them as special cases and at certain conditions other known equations such as the mass-energy equivalence equation ( E = m c² ) , Newton’s law of universal gravitation F = -\frac {\left (G m_ 1 m_ 2 \right)} {r^2}\hat {r}  , and Maxwell’s equations

The Einstein equations with the cosmological constant added are: eins-eq-cosmo-cstThe left-hand side of the field equations without the cosmological constant is the Einstein tensor , and the right-hand side is the constant χ multiplied by the stress-energy tensor.

Here are some more details about the elements of the equation (which represents a set of partial differential  equations):

eins-eq-cosmo-cst01

 And here is the drawing for the Dirac equation:

dirac-eq04f

I’ve placed in the middle of the drawing the condensed simple form of the Dirac equation with the partial differential symbol ∂ in Feynman slash notation . The background of the picture pertains to particle physics , particle accelerators and quantum mechanics , which are domains where the Dirac equation is used and applied.

Here is a brief description of this equation :

dirac-eq-01

At the top one can see the expanded  Dirac equation ( in terms of the gamma matrices ) written around the 3 D ring . Any similarity with the ring from ‘The lord of the rings’ novel and movies is unintentional.

Finally , here is a  nice looking 3D surface I obtained with Mathematica and customized with Photoshop. It took a little more time to render but I think it was worth it. I was inspired by the book  ‘Graphics with Mathematica  Fractals, Julia Sets, Patterns and Natural Forms ‘ , and I made my own modifications and changes to the Mathematica input and output . Click on the picture to see an enlarged version.

3dcurve-fractpers2

 The Mathematica code for the surface is:

fract-curve-code

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