# Energy conditions and non-physical phenomena

• I
accdd
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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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".

vanhees71 and accdd
accdd
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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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.

vanhees71 and accdd
accdd
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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