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Some helper worksheets for my projects.

3x3 transform dof decomposition

ADM Bona-Masso Eigenvectors

ADM Bona-Masso Inverse Eigenvectors

ADM connections




Curvature From Lower Dimensions

Differential Geometry/0 - curves

Differential Geometry/0 - tensors - intro

Differential Geometry/1 - index notation

Differential Geometry/1.1 - spinors

Differential Geometry/1.5 - wedge product

Differential Geometry/10 - Ricci curvature

Differential Geometry/11 - Gaussian curvature

Differential Geometry/12 - Bianchi identities

Differential Geometry/12.5 - Einstein tensor

Differential Geometry/12.7 - perpendicular spaces

Differential Geometry/12.8 - normal projections

Differential Geometry/13 - Einstein-Hilbert action

Differential Geometry/14 - ADM formalism

Differential Geometry/15 - ADM constraints

Differential Geometry/16 - ADM tetrad

Differential Geometry/17 - Palatini action

Differential Geometry/17b - Einstein-Cartan action

Differential Geometry/18 - Self-dual Palatini action

Differential Geometry/19 - Ashtekar variables

Differential Geometry/2 - structure constants

Differential Geometry/3 - exterior derivative

Differential Geometry/3.5 - Lie derivative

Differential Geometry/4 - metric tensor

Differential Geometry/5 - Levi-Civita tensor and Hodge dual

Differential Geometry/5.5 - Quaternions

Differential Geometry/6 - covariant derivative

Differential Geometry/7 - torsion

Differential Geometry/8 - metric-cancelling and torsion-free connection

Differential Geometry/8.1 - constant-metric connection

Differential Geometry/8.5 - parallel propagators

Differential Geometry/8.6 - parallel propagators and Riemann curvature

Differential Geometry/9 - Riemann curvature

Differential Geometry/9.3 - conformal connection

Differential Geometry/9.5 - perturbations

Differential Geometry/sources

Divergence Theorem in Spherical Coordinates

EFE Hyperbolic 4 form

EMHD Hyperbolic Conservation Laws

EMHD Linear Stability Analysis

Earth Rotation Geodesic Twisting

Einstein Equations, Weak Field, De-Donder Gauge

Einstein-Maxwell Hyperbolic Conservation Laws

Electromagnetism/0 - intro

Electromagnetism/1 - Faraday tensor in special relativity

Electromagnetism/2 - Faraday tensor in GR ADM in vacuum with E and B as vectors

Electromagnetism/2.5 - Faraday tensor in GR ADM in vacuum with E and B as one-forms

Electromagnetism/3 - Faraday tensor as 2-form

Electromagnetism/4 - electromagnetic stress-energy in vacuum

Electromagnetism/5 - electromagnetism in medium

Electromagnetism/Electromagnetic Tensor Self-Dual

Electromagnetism/Maxwell Equations - Eigenmode Analysis

Electromagnetism/Maxwell equations in hyperbolic form

Electromagnetism/Maxwell in inhomogeneous medium

Electromagnetism/Maxwell octonions

Electromagnetism/Relativistic Electromagnetism metric

Equations of Structure - Schwarzschild

Error in most CFD literature

Euler Fluid Equations - Curved Geometry - Contravariant

Euler Fluid Equations - Curved Geometry - Covariant

Euler Fluid Equations - Eigenmode Analysis 2

Euler Fluid Equations - Eigenmode Analysis

Euler Fluid Equations - Entropy Function

Finite Volume Methods

GEM force on a rotating object

GR EM Metrics/complex metric of EM potential

GR EM Metrics/complex metric of g + F

GR EM Metrics/complex metric of g + dual F

GR EM Metrics/curved space gravitomagnetics

GR EM Metrics/flat space gravitomagnetics

GR EM Metrics/metric of curved space and EM potential

GR EM Metrics/metric of flat space and EM potential

Gravitation 22.2

Kaluza-Klein - constant scalar

Kaluza-Klein - varying scalar

Kaluza-Klein - without cylindrical constraint

Kerr Cartesian

Kerr geodesic




MHD - Eigenmode Analysis


Measure of Any Simplex in Any Dimension

Metric Eigenmodes 2

Metric Eigenmodes

Metric for extruded dimension

Navier-Stokes As Exterior Derivative

Navier-Stokes Curl Advection



Numerical Relativity/1 intro

Numerical Relativity/2 list of formalisms

Numerical Relativity/3 adm

Numerical Relativity/3.1 adm with V

Numerical Relativity/3.1.1 adm with V - eigenfields

Numerical Relativity/3.2 adm with Gamma

Numerical Relativity/Z4 From Killing Vectors

Numerical Relativity/adm from efe

Numerical Relativity/bssnok-chi

Numerical Relativity/bssnok-scalar

Numerical Relativity/bssnok

Numerical Relativity/eigenwhatever

Numerical Relativity/equal up to principal part

Numerical Relativity/trace-free

Numerical Relativity/z4-with-conns

Numerical Relativity/z4-with-hyperbolic-gamma-driver-and-metric-free

Numerical Relativity/z4-with-hyperbolic-gamma-driver

Numerical Relativity/z4

PDE Systems, Parallel Propagators, Finite Volume

Platonic Solids

Quantum Computing


Riemann From Stress-Energy


Schwarzschild with mass varying with time

Shallow Water

Solving Connections From Riemann


Tetrad General Relativity

Tetration Derivative

Two-Fluid Plasma and GEM/0 - following Tajmar and De Matos paper

Two-Fluid Plasma and GEM/1 - GEM

Two-Fluid Plasma and GEM/2 - GEM Maxwell equations

Two-Fluid Plasma and GEM/3 - connections and GEM acceleration

Two-Fluid Plasma and GEM/4 - stress-energy from EM

Two-Fluid Plasma and GEM/5 - stress-energy from matter

Two-Fluid Plasma and GEM/6 - GLM Maxwell derivation

Two-Fluid Plasma and GEM/7.1 - cyclotron frequency

Two-Fluid Plasma and GEM/7.2 - normalized units

Two-Fluid Plasma and GEM/8 - two-fluid plasma model

a note on the definition of tensors


conformal Levi-Civita geodesic

gauge covariant derivative

heat to wave

how transforming pde state variables affects wavespeeds

hyperbolic rotations

magnetic field from a boosted charge

projection in any metric

removing beta from adm metric


stress-energy tensor

tensor product permutations

torsion gravity

twisted spacetime

wave equation hyperbolic form

wave equation in curved spacetime - finite difference





Putting my math in one place. See the README for CDN links.






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