A relação da energia do campo gravitacional com a hipersuperfície de simultaneidade

Abstract

The concept of energy is one of the most important in Physics, as it allows us to interpret and describe various physical phenomena. However, a good definition of the energymomentum tensor of the gravitational field is a big problem, if not an impossibility, that General Relativity presents.To try to understand this problem, this work used the Hamiltonian formulation of General Relativity, the so-called ADM formalism, which provides well-defined results for energy and momentum for asymptotically flat spacetimes. In this research, the plane wave spacetimes, Schwarzschild spacetimes and the FLRW model were analyzed; for both cases, both energy and momentum were obtained. On analysis, it was found that the ADM formalism for the Schwarzschild case and the cosmological model provides compatible results with those found in the literature; furthermore, it is shown that for plane wave spacetimes, inconsistencies arise from the ADM formalism, when compared with results provided by Teleparallelism Equivalent to General Relativity.