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

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.

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

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.

Gravitational waves, while detected by LIGO and predicted to carry energy, present a challenge in general relativity because covariant definitions based on stress energy yield zero energy for pure gravitational waves.

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.

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.

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.