# ADM formulation Initial Value Problem data per spacepoint

Gold Member
Homework Statement:
See attached screenshot of MTW pp 532/533
Relevant Equations:
N/A
I'm having a bit of trouble getting a clear picture of what is going on here, so if anyone can shed any light, it will be greatly appreciated.

1. I can see how the metric coefficients provide the six numbers per spacepoint, but it can't always be possible to transform the metric into a diagonal form can it?

2. The forward motion in time demands one number per spacepoint, which I assume is the value ##\bar t##. How is this 'already willy-nilly' present in the three data per spacepoint? Is it because the various ##g_{ij}## are functions of t, x, y and z so knowing a ##g_{ij}## and its co-ordinates, t follows?

4. Why 'In conclusion...' do we now have TWO data per spacepoint telling us about the ##^{(4)}\mathcal G## and what are they?

5. What has happened to the six ##\frac {\partial g_{ij}}{\partial t} ##?

Regards

TerryW

#### Attachments

• Data per spacepoint.png
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