The coordinates ##u## and ##v## are defined as ##u=t+r*##, ##v=t-r*##, where ##r*=r+2M In(\frac{r}{2M}-1)##.(adsbygoogle = window.adsbygoogle || []).push({});

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 questionis 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.

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# Extension of Schwarzschild light cones white hole/black hole

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