We address the issue of gravitational radiation in the context of the Bondi-Sachs space-time, and consider the expression for the gravitational energy of the radiation obtained in the realm of the teleparallel equivalent of general relativity (TEGR). This expression is independent of the radial distance (i.e., of powers of <math><mn>1</mn><mo>/</mo><mi>r</mi></math>) and depends exclusively on the functions <math><mi>c</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>θ</mi><mo>,</mo><mi>ϕ</mi><mo>)</mo></math> and <math><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>θ</mi><mo>,</mo><mi>ϕ</mi><mo>)</mo></math>, which yield the news functions (u is the retarded time, <math><mi>u</mi><mo>=</mo><mi>t</mi><mo>−</mo><mi>r</mi></math>). We investigate the mathematical and physical features of this energy expression in the simpler framework of axial symmetry. Once a burst of gravitational radiation takes place in a self gravitating system, that leads to a loss of the Bondi mass, gravitational radiation is emitted throughout the whole space-time. The existence and presence of this radiation in the background structure of the space-time is consistent with the analysis developed by Papapetrou, and Hallidy and Janis, who found no proof that a gravitational system that emits a burst of gravitational radiation is preceded and followed by two stationary gravitational field configurations, namely, it seems that it is impossible for a gravitational system, which is initially stationary, to return to a stationary state after emitting a burst of axially symmetric gravitational radiation, in which case the space-time is not even asymptotically stationary. Therefore, it is plausible that the gravitational energy of radiation is present in the background structure of the space-time, and this is the energy predicted in the TEGR. This analysis leads us to conjecture that the noise detected in the large terrestrial gravitational wave observatories is intrinsically related to the background gravitational radiation.

Brazil

J.W. Maluf

F.L. Carneiro

S.C. Ulhoa

J.F. da Rocha-Neto

Energy of gravitational radiation and the background energy of the space-time

In this work, we present an exact analysis of the two-dimensional noncommutative hydrogen atom. In this study, the Levi-Civita transformation was used to perform the solution of the noncommutative Schrodinger equation for Coulomb potential. As an important result, we determine the energy levels for the considered system. Using the result obtained and experimental data, a bound on the noncommutativity parameter was obtained.

Canada

R.G.G. Amorim

B.C. Wang

E.C. Brenag

V.C. Rispoli

Exact Noncommutative Two-Dimensional Hydrogen Atom

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

J.S. da Cruz Filho

A.F. Santos

F.C. Khanna

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR), the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then, the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.

E.P. Spaniol

R. Gomes

A.E. Santana

On Regular Black Holes at Finite Temperature

Small violation of Lorentz and CPT symmetries may emerge in models unifying gravity with other forces of nature. An extension of the standard model with all possible terms that violate Lorentz and CPT symmetries are included. Here a CPT-even non-minimal coupling term is added to the covariant derivative. This leads to a new interaction term that breaks the Lorentz symmetry. Our main objective is to calculate the cross section for the <math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></math> scattering in order to investigate any violation of Lorentz and/or CPT symmetry at finite temperature. Thermo Field Dynamics formalism is used to consider finite temperature effects.

P.R.A. Souza

On Lorentz violation in + → + Scattering at Finite Temperature

Gravitons are described by the propagator in teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermofield Dynamics formalism. The gravitational Casimir effect and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.

T.F. Furtado

On Gravitational Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.

Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

In this paper we use the conformal teleparallel gravity to study an isotropic and homogeneous Universe which is settled by the Friedmann–Robertson–Walker metric. The conformal symmetry demands the existence of a scalar field which works as a dark field for this model. We solve numerically the field equations then we obtain the behavior of some cosmological parameters such as the scale factor, the deceleration parameter and the energy density of the perfect fluid which is the matter field of our model. The field equations, which we called modified Friedmann equations, allow us to define a dark fluid, with dark energy density and pressure, responsible for the acceleration in the Universe, once we defined an equation of state for the dark fluid.

J.G. Silva

On Friedmann–Robertson–Walker model in conformal teleparallel gravity

We present the quantization process for Schwarzschild space-time in the context of Teleparallel gravity. In order to achieve such a goal we use the Weyl formalism that establishes a well-defined correspondence between classical quantities which are realized by functions and quantum ones which are realized by operators. In the process of quantization we introduce a fundamental constant that is used to construct what we call the quantum of matter by the imposition of periodic conditions over the eigenfunction.