Energy Is Conserved in the Classical Theory of General Relativity

Abstract

The first law of thermodynamics states that energy is conserved. It is one of the most fundamental laws of physics and not one that you would expect many physicists to challenge, so it comes as a surprise to find that a growing number of cosmologists and relativists are doing just that. Of course any law of physics is subject to experimental verification and as new realms of observation are opened up we should require that previous assumptions including conservation of energy are checked. But the subject under question is not new physics in this sense. It is the classical theory of general relativity. Whether general relativity is correct is not the issue, although it has withstood all experimental tests so far. The question concerns whether energy is conserved in the classical theory of general relativity with or without cosmological constant as given be Einstein nearly 100 years ago. This is a purely mathematical question.