Conformal compactification


by paweld
Tags: compactification, conformal
paweld
paweld is offline
#1
Feb22-10, 12:28 PM
P: 256
Let's consider for example compactification of Minkowski spacetime or
Kruskal extension of Schwartzschild. They are quite similar because in both cases
we rescale the null direction.
I wonder why we always rescale the null direction, not simply x or t.
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Altabeh
Altabeh is offline
#2
Feb22-10, 03:47 PM
P: 665
Quote Quote by paweld View Post
Let's consider for example compactification of Minkowski spacetime or
Kruskal extension of Schwartzschild. They are quite similar because in both cases
we rescale the null direction.
I wonder why we always rescale the null direction, not simply x or t.
Re-scaling the null direction has this advantage that since one side is equal to zero, then the re-scaling factor won't change the direction but rather compacts (or maybe expands) the direction conformally. However, re-scaling x or t does not preserve the general form of metric though wouldn't change its nature, too if the re-scaling factor isn't coordinate-dependent! In the latter case (a factor being independent of coordinates), one can make use of the re-scaling of x or t as well!

AB


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