Monday, December 5, 2016
The following property is true in four spacetime dimensions   This property (property A from now on) can for example be used to obtain the metric and electromagnetic field of the Israel-Wilson-Perjés (IWP) black holes. Because I wanted to generalize the IWP black holes to higher dimensions, I wanted to find the generalization of property A in higher dimensions.
Monday, November 21, 2016
The usual way to obtain the metric and electromagnetic field of a charged black hole in general relativity is to make a spherically symmetric ansatz, insert this ansatz into the Einstein-Maxwell equations and then solve the resulting set of non-linear ordinary differential equations. In this post I explain an alternative method that uses Killing spinors. This method can be used for extremal black holes. These are black holes with charge equal to the mass.
Tuesday, October 11, 2016
While studying Lie-algebras I read that the three-dimensional harmonic oscillator has an $SU(3)$ symmetry. I found this very unexpected; I thought it was ''obvious'' that the symmetry is only $SO(3)$.
Thursday, October 6, 2016
The product of two irreducible representations of a simple Lie algebra can be decomposed into irreducible components. There are various techniques to calculate this decomposition, see for example chapter XIV in . However, the decomposition can also be calculated by brute force.