Energy conditions and non-physical phenomena

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accdd
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Is the inability to exceed the speed of light a consequence of general relativity?
Is the fact that no energy is created from empty space a consequence of general relativity?
Or are they both constructions deriving from the energy conditions imposed to have solutions to Einstein's equations that are compatible with observations?
 

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Orodruin
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Is the inability to exceed the speed of light a consequence of general relativity?
You need to define what you mean by "exceeding the speed of light".
Is the fact that no energy is created from empty space a consequence of general relativity?
You need to define what you mean by "no energy is created from empty space".
 
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  • #3
accdd
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Locally, nothing can exceed the speed of light.
If I take a small volume I don't expect it to generate stuff out of a vacuum.
 
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Orodruin
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Locally, nothing can exceed the speed of light.
This in essence follows from 4-momentum being non-spacelike.

If I take a small volume I don't expect it to generate stuff out of a vacuum.
This, in the form ##\nabla_\mu T^{\mu\nu}## is a direct consequence of varying the Einstein-Hilbert action with an additional term to describe the matter fields (and thereby generating the stress-energy tensor). The Einstein field equations resulting from varying the Einstein-Hilbert action are on the form ##G_{\mu\nu} = C T_{\mu\nu}##, where ##C## is a constant and the divergence of the Einstein tensor ##G_{\mu\nu}## is equal to zero.

However, "global" energy is generally not conserved in general relativity as demonstrated, e.g., by FLRW cosmologies.
 
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Sean Carroll in Spacetime and Geometry writes (4.6, last section):
[Energy conditions ... serve to prevent other properties that we think of as "unphysical", such as energy propagating faster than the speed of light...]
What does this means?
 
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Orodruin
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I suggest looking at the basic descriptions of different energy conditions in relativity. They are all concerned with the stress-energy tensor and are at varying degrees of strictness. For example, look at https://en.wikipedia.org/wiki/Energy_condition under "Mathematical statement".

The statement that relates to the flow of energy is the dominant energy condition which relates to ##T_{ab} Y^b## where ##Y## is a time- or light-like vector field. The resulting 4-vector describes energy density and flow.
 
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