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Trajectories in the Schwarzschild space-time

Using the Riemann package presented in a previous post, one can easily perform basic computations in General Realtivity. In this post, I am going to show how it can be used to compute the geodesics of the Schwarzschild space-time.

An example in using the Riemann package

I have written a Mathematica package to perform basic computations in Riemannian geometry. In this post, I share an example of computation that this code can be used for and a link to the package containing the instructions to reproduce the computation presented here.

Using flexible input files in Fortan

I created a way to parse input files to Fotran more flexibly. The code is available in a dedicated git repository. In this post, I go through some of the details of most of the code blocks.

What is the distance to the horizon ?

I compute the distance of the horizon to an observer on the shore using trigonometry. I try to give a solution that is slightly more accurate than the classic way of the classic one based on Pythagora's theorem and compare the two results.

The rubber band theorem

I share a practical experiment of differential geometry by looking at two rubber bands on a table. This provides an opportunity to illustrate a theorem about the total curvature of closed curves.

The decimal point is ambiguous

A short post about the ambiguous nature of the decimal point. This illustrates how a number shouldn't be confused with its graphical representation.

Kinematic in a rotating reference frame

The equations that describe the dynamics of a point particle in space must be adapted when the motion is observed from an accelerated frame of reference. I give an illustration of this by considering the motion of a free particle relative to a frame rotating at a constant angular velocity around the origin of coordinates.

Geometry on a curved space

Euclid's axioms describe the geometry of shapes and curves in simple mathematical spaces which are called *flat*. When one considers more complex spaces, these axioms are no longer adequate. I illustrate this by looking at the special case where the mathematical space is a *two-sheet hyperboloid*.

What happens when you try to reach the speed of light ?

I talk about the mathematics describing what happens when a massive objects is accelerated at a steady rate and how it behaves when its velocity approaches that of light using the principles of special relativity.