Energy-momentum and angular-momentum of a gyratonic pp -waves spacetime

Abstract

Gyratonic plane fronted gravitational waves are exact solutions of Einstein's field equations, which correspond to gravitational waves that carry momentum and angularmomentum. Using the definitions of the Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, we explicitly evaluate the general expressions of the energymomentum and angular-momentum of these space-times. In order to better understand the additional properties of these gravitational waves, we consider the motion of particles in this space-time and obtain an interesting relation between the angular-momentum of the particles and that of the gravitational waves.

Sobre ondas gravitacionais planas não-lineares

“…A métrica transversa dada pela equação (38) permite a descrição das congruências nulas no espaço-tempo curvo. Ela possui algumas propriedades, sendo elas que h µν 1.é ortogonalà k µ , i.e., h µν k µ = 0; 2.é ortogonalà N µ , i.e., h µν N µ = 0; 3. possui traço 2, i.e., h µ µ = 2; 4. projetado nele mesmo gera ele mesmo, i.e., h µ ρ h ρ ν = h µ ν .…”

“…Entretanto, como o efeito gravitacionalé um efeito global, conforme visto na seção 2.3, não se pode argumentar que os campos gravitacionais sejam equivalentes. Pesquisas sobre as ondas giratônicas dentro do TERG levaram a obtenção de propriedades qualitativas distintas entre esses espaçostempo [38], corroborando a distinção entre os campos gravitacionais. Destarte, o estudo das ondas gravitacionais planas fornece não apenas um campo de estudo introdutório para a RG, mas também um campo aberto de pesquisa para a investigação de resultados ainda não bem compreendidos na gravitação como um todo.…”

On the quantization of Burgers vector and gravitational energy in the space-time of a conical defect

“…One of the most interesting results is that the particle extracts a discrete amount of energy of the defect. The possibility that the energy (and also angular momentum) acquired by the particle comes from the gravitational field had already been contemplated in the case of a particle interacting with a gravitational wave [20,21].…”

“…After projecting the torsions (21)(22)(23) into the tangent space, we obtain the non-vanishing Σ (0)bc components as…”

A global distinct pp-wave spacetime

“…Some symmetries and invariants of the so-called gyratonic waves were studied in these references, and an important work reviewing some previous works and extending the study for impulsive waves was made by Podolsky and collaborators [25]. Like the standard pp-waves, the gyratonic waves also have a flat wavefront and interact with particles, exchanging energy and angular momentum [26]; also its gravitational energy is distinct from that of the standard pp-waves, configuring a generalized pp-waves spacetime [27]. Thus, the pp-waves are an open field of study.…”