Is energy conserved in general relativity ?

Abstract

This short report is dedicated to the 40th anniversary of International Journal of Modern Physics A (IJMPA) and Modern Physics Letters A (MPLA). While the report is based on a series of papers[1-8], its content reflects my personal viewpoints. Therefore I am solely responsible for all the statements in the report. In this report we discuss conservation of energies in a curved spacetime including general relativity. We argue that the matter energy is not necessarily conserved in a curved space time due to a lack of time translational invariance, and adding energy of gravitational fields to recover the conservation law of energies fails due to Noether's 2nd theorem. We show that there exists conserved quantities associated with the matter energy momentum tensor other than the energy in a curved spacetime, and discuss consequences of the existence of such conserved charges.

15 pages, 1 figure, a sentence added in the abstract

References in corpus (6)

• On the Distributional Nature of the Energy Momentum Tensor of a Black Hole or What Curves the Schwarzschild Geometry ?
• Conserved charges in general relativity
• Essential core of the Hawking--Ellis types
• Criteria for energy conditions
• Conserved non-Noether charge in general relativity: Physical definition vs. Noether's 2nd theorem
• Noether's 1st theorem with local symmetries