Notes: Magnetostatic multipole expansion using STF tensors
How to do the STF multipole expansion of the magnetic potential and field (it’s been on my TODO list for a while)
Notes
#2023
#2021
Notes: How to take a derivative of a generalized continued fraction
So you have a function in terms of a continued fraction, and you want to compute its derivative…
#2020
Notes: Generalized harmonic form of Einstein’s equations from a gauge-fixed action
The generalized harmonic formulation can be derived by adding a gauge-fixing term to the Einstein-Hilbert action
#2019
Notes: A family of ramp functions and the Beta function
Sometimes in a numerical method, you need to be able to continuously turn a calculation on or off in space or time.
#2018
(Notes) When is a metric conformal to Ricci-flat?
Integrability conditions when trying to solve for a conformal factor
#2017
Note on simple(r) equations for Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons theories
Here to save you some algebra and column-inches
Note on commutation coefficients in two ways
An identity between vector commutation coefficients and coframe connection coefficients
Note on exterior, interior, and Lie derivative superalgebra
These three objects form a superalgebra! Whoa!
Note on Lie derivatives and divergences
When can you integrate-by-parts with Lie derivatives?
Note on generating a divergence identity
Special thanks to Ben Mares for coming up with this identity.
Note on a (dimension-dependent) Weyl identity
There is a nice 4-dimensional Weyl identity that I can never seem to remember off the top of my head; so I decided I need to write this note so I don’t have ...
Notes on the Weyl, E/B, and 3+1 decompositions of Riemann, and curvature invariants
The Weyl decomposition, further splitting into E/B, and computing in terms of 3+1 objects
Notes on the pullback connection
In an effort to keep myself organized, I decided I should type up some notes I have laying around.