How do conservastion laws operate in a gravitational field?

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Offline jeffreyH

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The conservation of angular momentum is said to be due to the isotropy of space and the conservation of energy is due to the homogeneity of time. How do conservation laws then apply to space and time in a gravitational field and is this strictly observer dependent?
Fixation on the Einstein papers is a good definition of OCD.

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Offline PmbPhy

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I'm not sure but in cases like angular momentum they only apply locally. I think that if the spacetime curvature is zero and thus space is homogeneous but there's a g-field present then it may still apply but I don't know whether or not it does.
« Last Edit: 01/03/2015 20:28:46 by PmbPhy »

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Offline jeffreyH

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I am going to try to dig a bit deeper into this one. I have no idea where I will find any information but if I get anything I'll post it here.
Fixation on the Einstein papers is a good definition of OCD.

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Offline JohnDuffield

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The conservation of angular momentum is said to be due to the isotropy of space and the conservation of energy is due to the homogeneity of time. How do conservation laws then apply to space and time in a gravitational field and is this strictly observer dependent?
You'll get various answers to this. Some will say energy is not conserved, whilst I say it is. I imagine most people will say angular momentum is conserved, whilst I say it isn't.

I say that because the "coordinate" speed of light at the event horizon, as measured by distant observers, is zero. And nothing can move faster than light, so at that location, any rotation rate has to be zero too. This doesn't sit too well with the Kerr Metric, but what can I say?

Note that in his Leyden Address Einstein described a gravitational field as a place where space is "neither homogeneous nor isotropic".   
« Last Edit: 02/03/2015 14:18:54 by JohnDuffield »