R/penrose_cauchy.R

In RobinHankin/schwarzschild: General Relativity in R

penrose_cauchy <- function(colours=standard_colours, ...){

  ## plots a Penrose diagram of the whole universe.  We can choose colours

  penrose <- penrose_transform("cauchy")

  ## set up axes
  jj <- c(-1,1)
  plot(jj,jj,asp=1,type='n',axes=FALSE,xlab='',ylab='',main='Cauchy transform')

  ## plot 'boundary' of universe

  segments(x0=c(-1,0,1,0),
           y0=c(0,1,0,-1),
           x1=c(0,1,0,-1),
           y1=c(1,0,-1,0),
           col='gray'
           )

  ## some annotation
  text(0,1.03,'distant future')
  text(0,-1.03,'distant past')
  text(-1.1,0,'far\n away\n left')
  text(1.1,0,'far\naway\nright')

  o <- seq(from=0,to=1,len=5)

  ## now a key:
  for(i in o/10 +0.95){segments(x0=-1.1,x1=-1,y0=i,y1=i,col=colours$spacelike_curve)}
  text(-1,1,"spacelike curves",pos=4)

  for(i in o/10 - 1){segments(x0=i-0.1,x1=i-0.1,y0=0.75,y1=0.85,col=colours$timelike_curve)}
  text(-1,0.8,"timelike curves",pos=4)

                                        #for(i in o/10/sqrt(2)){segments(x0=-1.05+i,x1=-1.1-0.05/2+i,y0=0.55+i,y1=0.6+0.05/2+i,col=colours$photon)}
  for(i in o/10/sqrt(2)){segments(x0=-1.05-i,x1=-1+0.05-0.05/2-i,y0=0.55+i,y1=0.6+0.05/2+i,col=colours$photon)}
  text(-1,0.6,"null curves",pos=4)

  ## first timelike vectors:

  jj <- c(-1000,seq(from= -20,to=20, len=1000),1000)

  ##thingvec <- seq(from=-18,to=18,by=1)
  thingvec <- seq(from=-6,to=6,by=0.25)

  for(i in thingvec){
    ## first timelike vectors:
    xt <- cbind(x=i,t=jj)
    points(penrose(xt),type='l',col=colours$timelike_curve)

    ## now spacelike vectors
    xt <- cbind(x=jj,t=i)
    points(penrose(xt),type='l',col=colours$spacelike_curve)
  }

  if(FALSE){
                                        # plot some null curves, all emitted at the same time:

    start_time <- -2
    end_time <- 100
    
    for(i in thingvec){
      points( penrose(
          cbind(x=c(i,i+end_time),
                t=c(start_time,  start_time + end_time)
                )
          
      ),col=colours$photon,type='l')
    }
    
  }


                                        # plot some null curves, all emitted at the same time:
  start_x <- -1
  end_time <- 100

  for(i in thingvec){
    points( penrose(
        cbind(x=c(start_x,start_x+end_time),
              t=c(i, i+end_time)
              )
        
    ),col=colours$photon,type='l')
  }
  ## plot the AUT logo:
  if(!isFALSE(getOption("schwarzschild_logo"))){logo(x=0.85,y=0.20, width=0.1)}

  git(-1.2,-1.1)
  
}