arrows: Arrows on worldlines and null geodesics

In RobinHankin/schwarzschild: General Relativity in R

Arrows on worldlines and null geodesics

Description

Helper functions that plot arrows on worldlines and null geodesics, with functionality to make sure that the arrows are in the right direction

Usage

raindrop_arrow(r,offset=0, ...)
ingoing_null_arrow_eddington_ingoing_coords(r, offset, colours=standard_colours, ...)
ingoing_null_arrow_eddington_outgoing_coords(r, offset, colours=standard_colours, ...)
outgoing_null_arrow_eddington_ingoing_coords(r, offset, colours=standard_colours, ...)
outgoing_null_arrow_eddington_outgoing_coords(r, offset, colours=standard_colours, ...)

Arguments

r	Schwarzschild radius
offset	Controls vertical position of arrow; see details
colours	List of colours
...	Further arguments, passed to arrows()

Details

An arrow is drawn at event (r,t) where Schwarzschild r is specified by argument r. The functions take an offset argument that ensures that ingoing or outgoing null geodesics reach the singularity at tdash=offset. This makes it easy to place several arrows on the same null geodesic (or worldline in the case of raindrop()).

The idea is that

• ingoing_null_arrow_eddington_ingoing_coords(r=2, offset=3)

• ingoing_null_arrow_eddington_ingoing_coords(r=2, offset=4)

• ingoing_null_arrow_eddington_ingoing_coords(r=2, offset=5)

(executed while the output of eddington() is active the active device), plot arrows which are vertically aligned at r=2 and are placed on ingoing null geodesics which reach the singularity at tdash=3:5. Conversely:

• ingoing_null_arrow_eddington_outgoing_coords(r=2.0, offset=4)

• ingoing_null_arrow_eddington_outgoing_coords(r=2.3, offset=4)

• ingoing_null_arrow_eddington_outgoing_coords(r=2.6, offset=4)

will give arrows which are all on the same null geodesic (specifically, the one that reaches the singularity at tdash=4.

Author(s)

Robin K. S. Hankin

Examples

## Not run: 
eddington()
outgoing_null_arrow_eddington_ingoing_coords(r=2,offset= -1)
outgoing_null_arrow_eddington_ingoing_coords(r=2,offset=  0)
outgoing_null_arrow_eddington_ingoing_coords(r=2,offset= +1)

## End(Not run)

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