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.

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.

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.

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.

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.

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

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 Schwarzschild black hole is often called a vacuum solution, but it actually contains a delta function singularity, indicating that it isn't truly a vacuum.

Using the time-like Killing vector outside the horizon of a black hole allows for the correct determination of the black hole's mass, despite the singularity. The ADM mass, which I refer to as E sub A, combines total rest mass and gravitational binding energy, but it differs from the regular energy E, which is covariant and relies on asymptotic flatness.

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.

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.

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.

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.