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.

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

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

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.

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.

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

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.

General Relativity is based on two foundational pillars: general covariance, meaning physical laws don't depend on coordinate choices, and the principle of equivalence, which states that gravity is the same as local acceleration.