penrose: Penrose diagrams

In RobinHankin/schwarzschild: General Relativity in R

Penrose diagrams

Description

Penrose diagrams of the universe either with or without a black hole, using different transforms.

Usage

penrose_cauchy(colours=standard_colours, ...)
penrose_laplace(colours=standard_colours, ...)
penrose_logistic(colours=standard_colours, ...)
penrose_norm(colours=standard_colours, ...)
penrose_BH_cauchy(colours=standard_colours, ...)
penrose_BH_laplace(colours=standard_colours, ...)
penrose_BH_logistic(colours=standard_colours, ...)
penrose_BH_norm(colours=standard_colours, ...)
penrose_BH_extended(colours=standard_colours, ...)
penrose_transform(choice)
penrose_transform_backward(choice)

Arguments

colours	colours argument, a list
choice	In function penrose_transform(), argument choice is a string specifying the name of the statistical distribution used to define the transform. Current choices are Cauchy, normal (Gaussian), logistic, laplace; see details section
...	Further arguments, currently ignored

Details

A Penrose transform uses a map from the real line to the interval (-1,1). Function penrose_transform() returns one of several Penrose transformations. The forward transform maps the real line to the interval (-1,1) and the backward transform is the inverse of this. Argument choice specifies a statistical distribution. The forward transform uses the distribution's cumulative distribution function (CDF) F(\cdot), but because the CDF maps to (0,1) rather than the desired (-1,1) it maps x to 2F(x)-1. The backward transform uses the distribution's quantile function Q(\cdot), mapping x to Q((x+1)/2).

If the name of a function includes “_BH_”, for example penrose_BH_norm(), then the diagram includes a black hole.

Value

Functions penrose_foo() and penrose_BH_foo() are executed for the side-effect of plotting a graph. Function penrose_transformation() returns a function which gives the appropriate Penrose transform.

Note

Although these functions can be called directly, they are designed to be called by inst/maker.R, which produces correctly-sized and annotated PDF diagrams.

Author(s)

Robin K. S. Hankin

Examples

penrose_cauchy()
penrose_laplace()
penrose_logistic()
penrose_norm()

penrose_BH_cauchy()
penrose_BH_laplace()
penrose_BH_logistic()
penrose_BH_norm()

penrose_BH_extended()

RobinHankin/schwarzschild documentation built on Nov. 13, 2024, 12:58 p.m.