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.

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

K =  Kretschmann_scalar(r,θ,a)

Kretschman scalar for the Kerr metric

PlotTrajectory(solution,model,dimensions=[1,2,3],savepath="")

Plot trajectory of a body. Assumes coordinates are Boyer Lindquist. Plots in either 2D or 3D depending on specification of dimensions. Saves a low resolution PNG figure to disk in example_media/

StackedPlot(solution,model,savepath="")

Plot the x-y and x-z trajectory of a body on two separate subplots

bounds_checks(P)

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

l = calculate_levi(NF)

Determine the Levi-civita psuedo tensor

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

g=covariant_metric(coords,a)

Construct the NxN matrix of 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

d = mapping_d(r,a,zminus)

Mapping function d used when converting from Keplerian orbital parameters to constants of motion

f = mapping_f(r,a,zminus)

Mapping function f used when converting from Keplerian orbital parameters to constants of motion

g = mapping_g(r,a)

Mapping function g used when converting from Keplerian orbital parameters to constants of motion

h = mapping_h(r,a,zminus)

Mapping function h used when converting from Keplerian orbital parameters to constants of motion

g = metric_g11(coords,a)

The covariant tt component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g14(coords,a)

The covariant tϕ component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g22(coords,a)

The covariant rr component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g33(coords,a)

The covariant θθ component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g44(coords,a)

The covariant ϕϕ component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g11(coords,a)

The covariant tt component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g14(coords,a)

The covariant tϕ component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g22(coords,a)

The covariant rr component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g33(coords,a)

The covariant θθ component of the Kerr metric in Boyer Lindquist coordinates

g = metric_g44(coords,a)

The covariant ϕϕ component of the Kerr metric in Boyer Lindquist coordinates

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/parameters.jl.

ϵ = permutation_tensor(metric)

Calcualte the Levi-civita tensor in an arbitrary basis.

R = riemann(coords,a)

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

R = schwarzchild_covariant_riemann(coords,a)

Special case - the fully covariant components of the Riemann tensor for schwarzchild metric Used for testing

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