# Energy in Gravitation and Noether's Theorems

## TL;DR

This paper discusses the conflicting roles of Noether's theorems in defining energy within General Relativity, emphasizing the necessity of breaking general covariance to recover global symmetries and conserved quantities.

## Contribution

It clarifies how boundary conditions break coordinate invariance, enabling the application of Noether's first theorem to define energy in gravitational theories.

## Key findings

- Boundary conditions break coordinate invariance.
- Global symmetries re-emerge in special cases.
- Energy definitions depend on boundary choices.

## Abstract

I exhibit the conflicting roles of Noether's two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that removes the barrier her second theorem otherwise poses to the applicability of her first. There is nothing new here, except the emphasis that General must be broken down to Special Relativity in a special, but physically natural, way in order for the Poincare or other global groups such as (A)dS to "re-"emerge.