# 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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