Most realistic cosmological spacetimes lack exact Killing vectors, limiting the applicability of the clean definition of energy in General Relativity.

Defining energy in general relativity is complex; pseudotensors can provide conservation but break covariance, while covariant definitions work under symmetry but fail in general spacetimes, hinting at a deeper structure yet to be universally interpreted.

In flat spacetime, energy-momentum conservation is straightforward, but in General Relativity, it becomes complex due to the need for a covariant derivative and additional machinery.

In the context of the expanding universe, the standard energy is not conserved as energy gets diluted, but a vector field can be found that satisfies conservation conditions, leading to a conserved quantity related to entropy.

Definitions of energy, such as mass in motion or the capacity to change, don't hold up in dynamically curved spacetime.

Einstein introduced the pseudotensor to represent the energy of the gravitational field, but it depends on chosen coordinates, which contradicts the principle of general covariance.

Spacetime can be visualized as a four-dimensional construct where time is treated as another dimension, but as three-dimensional beings, we struggle to fully comprehend this concept, including the curvature of spacetime caused by mass and energy. While I can mathematically suppress one of the spatial dimensions and draw it, we misrepresent spacetime in our drawings, even though we understand the rules for adding distances on this misrepresentation.

The energy associated with gravity is coordinate-dependent, raising questions about whether this is a valid justification for using the pseudotensor.

Maxwell's equations are conformally invariant, meaning they depend on the space-time structure independent of scaling.