# Energy conditions and non-physical phenomena

• I
• accdd
In summary: This condition is quite strict and is not violated in general relativity.The fact that no energy is created from empty space is also a consequence of the stress-energy tensor. But it is not a strict condition as it is violated in the presence of a source of energy. In particular, the vacuum energy is not zero.

#### 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?

accdd said:
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".
accdd said:
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
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.

accdd said:
Locally, nothing can exceed the speed of light.
This in essence follows from 4-momentum being non-spacelike.

accdd said:
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
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?

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.

vanhees71 and accdd

## What are energy conditions?

Energy conditions refer to a set of mathematical inequalities that are used in general relativity to describe the distribution and flow of energy and matter in the universe. These conditions are used to constrain the behavior of matter and energy in different regions of space and time.

## What is the importance of energy conditions in physics?

Energy conditions play a critical role in understanding the behavior of matter and energy in the universe. They help us make predictions and calculations about the curvature of spacetime and the formation of black holes. They also provide a framework for testing the validity of different theories of gravity and matter.

## What are the different types of energy conditions?

There are several types of energy conditions, including the dominant energy condition, the weak energy condition, and the strong energy condition. These conditions impose different constraints on the energy and matter content of a given region of space and time.

## Can energy conditions be violated?

While energy conditions are an important tool in understanding the behavior of matter and energy, they are not absolute laws and can be violated under certain circumstances. For example, in quantum field theory, it is possible for energy to be negative in certain regions of space. However, these violations are usually limited and do not negate the usefulness of energy conditions in general relativity.

## How do energy conditions relate to non-physical phenomena?

Energy conditions are primarily used in the study of physical phenomena, such as gravity and the formation of black holes. However, they can also be applied to non-physical phenomena, such as hypothetical concepts like warp drive or wormholes. In these cases, energy conditions are used to determine if these phenomena are physically possible according to our current understanding of physics.