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The research aims to clarify the conditions under which energy conservation can be defined in general relativity.

July 13, 2026Open Access

Energy Conservation in General Relativity: Killing Fields, Conformal Charges, and the Scope of Noether's Theorems

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The research aims to clarify the conditions under which energy conservation can be defined in general relativity.
Analyzed two routes for energy conservation using Noether's theorems including the contracted Bianchi identity and the B4Diff(C2M) Noether identity.
Investigated the implications of Killing fields and transient sources on conserved charges in globally hyperbolic spacetimes.
Explored various mass definitions and their compatibility with general relativity.
Demonstrated that the charge integral depends only on Killing fields on globally hyperbolic spacetimes.
Showed that no local covariant gravitational energy density exists, meaning energy conservation in this framework is limited.
Identified Minkowski and Schwarzschild spacetime as key realizations of conservation cases and discussed the implications for models like Friedmann-Lemaître-Robertson-Walker cosmology.

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Examines energy conservation in general relativity, revealing limitations in forming energy laws.

Guo Chen (2026) studied this question.

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