Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo

Abstract

The presente dissertation delas with comparisons between two approaches for energyand Momentum of the gravitational field, namely, the Landau-Lifshitz pseudotensor and the energy-momentum tensor of teleparallelism. The problem of determining gravitational energy dates back to the emergence of general relativity in 1915. It is a problem of great importance for Physics, since the concepts of energy and momentum are fundamental both for classical theories and quantum mechanics. Understanding how the gravitational field behaves is fundamental to solving one of the biggest problems in modern physics, the con- struction of a quantum theory of gravitation; certainly, there solution of the gravitational field energy problem will help in this understanding. Due to the numerous approaches to solve this problem, it was not possible to make a detailed description of each one. Thus, we decided to work with only the Landau-Lifshitz pseudotensor and the telepar- allelism tensor. The Landau-Lifshitz pseudotensor is defined in the contexto of general relativity and is often used in textbooks when one wants to give a qualitative description of the gravitational field energy. The teleparallelism tensor we used was developed in the context of a theory that provides the same field equations as GR but has a notion of dis- tant parallelism; this theory is known as Teleparallelism Equivalent to General Relativity (TEGR). In this dissertation, we presente results that show that the teleparallelism tensor presentes more adequate properties to describe the gravitational field than the Landau- Lifshitz pseudotensor. We discuss, for example, the result that is already well known in the literature that the teleparallel version reproduces the equation of state of a massless field, while the Landau-Lifshitz pseudotensor is not always capable of such a feat.As an original result, we were able to show that for a weak field and with a suitable “gauge” choice the Landau-Lifshitz pseudotensor differs from the teleparallel one by a fourth order term. We also made exact comparisons in the spacetime of plane waves, known generically as pp-waves.