The relationship between matter and curvature in Einstein's equations suggests that only matter energy is well-defined, leaving the nature of energy in general relativity still unresolved after over a century of inquiry.

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.

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

If spacetime has symmetries, such as a timelike Killing field, it allows for the definition of genuinely conserved, coordinate-independent energy.

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.

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.

You probably don't know what energy is, and that's okay; even Einstein likely didn't fully grasp it in the context of General Relativity.

Physics professors often avoid discussing energy in General Relativity, similar to how a parent might skip the sex talk, because the topic is messy and unresolved.

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.