Index of all functions

C = Constants(P)

A struct to hold all variables which are constant over the course of the integration. These are derived from the user-defined parameters

Generator function for a Constants struct.

M = Model(P,C)

The model struct which holds all the parameters (P) and constants (C)

Struct holding the so-called 'prognostic' variables. 'Prognostic' terminology is borrowed from cliamte science where it refers to any variables that are predicted via integration

P = Parameters(kwargs...)

A struct to hold all model parameters that may be changed by the user. The struct uses keywords such that default values can be changed at creation. The default values of the keywords define the default model setup.

Plotting recipe for use with Plots.jl

E,L,Q = ELQ(a,α,e,ι,D)

Calculate the energy, angular momentum and Carter constant given the Keplerian orbital parameters, and the BH spin/direction Specific to the Kerr metric, see Schmidt 2002 arXiv:0202090

bounds_checks(P)

Look before you leap - are the user-specified kwargs in parameters physical and reasonable?

Γ = christoffel(coords,a)

The christoffel symbols of the Kerr metric. See e.g. https://arxiv.org/pdf/0904.4184.pdf

g=contravariant_metric(coords,a)

Construct the NxN matrix of the contravariant metric. Metric components are defined via indvidual functions to allow for auto diff in unit tests

p_{μ} = convert_to_covariant(metric,p^{μ})

Convert a vector from contravariant form to convariant form using the covariant metric

Δ = delta(r,a)

The well-known delta function of the Kerr metric

initialization = initial_conditions(M)

Setup the initial conditions for the MPD orbital dynamics

l = levi_civita_symbol(NF)

Determine the Levi-civita psuedo tensor

ϵ = levi_civita_tensor(metric)

Calcualte the Levi-civita tensor in an arbitrary basis.

solution,model = orbit(NF,kwargs...)

Runs RelativisticDynamics.jl with number format NF and any additional parameters in the keyword arguments kwargs.... Any unspecified parameters will use the default values as defined in src/system_parameters.jl.

R = riemann(coords,a)

Riemann tensor components of the Kerr metric. First index is the contravariant, others are covariant

Σ = sigma(r,θ,a)

The well-known sigma function of the Kerr metric

S^{μ ν} = spintensor(levi,pvector,svector,m0)

Calculate the contravariant spin tensor.

solution = timestepping(X,M)

The timestepping integration once all variables have been initialised