- #1
binbagsss
- 1,254
- 11
The coordinates ##u## and ##v## are defined as ##u=t+r*##, ##v=t-r*##, where ##r*=r+2M In(\frac{r}{2M}-1)##.
In ##u,r,\theta,\phi ## coordinates the radially null geodesics are given by:
##\frac{du}{dr}=0 ## for infalling,
##\frac{du}{dr}=2(1-\frac{2M}{r})^{-1} ## for outgoing.
In the ##v,r,\theta,\phi ## coordinate the radially null geodesics are given by:
##\frac{du}{dr}=0 ## for outgoing,
##\frac{du}{dr}=-2(1-\frac{2M}{r})^{-1}## for infalling.
For ##r<2M## it is clear that the ##(1-\frac{2M}{r})^{-1} ## term becomes negative.
Question:
So this results in the light cones on ##u## vs ##r## , first attachment, tilting over.
This explains why ##r \leq 2M ## is a black-hole, within this region as time increases ##r## can only decrease.
My question is in a similar way trying to explain why, attachment two, demonstrates a white-hole.
So here the light-cones do the opposite, for ##r>2M## as time increases ##r## decreases and within ##r \leq 2M ## as time increases ##r ## increases.
So the definition of a white hole is that no signal from infinity can enter - how should this be obvious from th light cones?
Thanks very much in advance.
In ##u,r,\theta,\phi ## coordinates the radially null geodesics are given by:
##\frac{du}{dr}=0 ## for infalling,
##\frac{du}{dr}=2(1-\frac{2M}{r})^{-1} ## for outgoing.
In the ##v,r,\theta,\phi ## coordinate the radially null geodesics are given by:
##\frac{du}{dr}=0 ## for outgoing,
##\frac{du}{dr}=-2(1-\frac{2M}{r})^{-1}## for infalling.
For ##r<2M## it is clear that the ##(1-\frac{2M}{r})^{-1} ## term becomes negative.
Question:
So this results in the light cones on ##u## vs ##r## , first attachment, tilting over.
This explains why ##r \leq 2M ## is a black-hole, within this region as time increases ##r## can only decrease.
My question is in a similar way trying to explain why, attachment two, demonstrates a white-hole.
So here the light-cones do the opposite, for ##r>2M## as time increases ##r## decreases and within ##r \leq 2M ## as time increases ##r ## increases.
So the definition of a white hole is that no signal from infinity can enter - how should this be obvious from th light cones?
Thanks very much in advance.