arXiv subjects
Publications and source records attributed to S. C. Ulhoa.
The paper deals with the problem of describing fundamental particles. The Einstein-Rosen approach was revisited to explain que charge-mass ratio quantization. Such a result is obtained once a quantization prescription is applied to the expression of gravitational energy defined in the realm of teleparallel gravity.
We construct the gravitational energy-momentum of the Bondi-Sachs space-time, in the famework of the teleparallel equivalent of general relativity (TEGR). The Bondi-Sachs line element describes gravitational radiation in the asymptotic region of the space-time, and is determined by the mass aspect and by two functions, $c$ and $d$, that yield the news functions, which are interpreted as the radiating degrees of freedom of the gravitational field. The standard expression for the Bondi-Sachs energy-momentum is constructed in terms of the mass aspect only. The expression that we obtain in the context of the TEGR is given by the standard expression, which represents the gravitational energy of the source, plus a new term that is determined by the two functions $c$ and $d$. We interpret this new term as the energy of gravitational radiation.
Symplectic unitary representations for the Poincaré group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
In this paper, we will study non-commutative corrections in the metric tensor for the Gödel-type universe, a model that has as its main characteristic the possibility of violation of causality, allowing therefore time travel. We also find that the critical radius in such a model, which eventually will determine the time travel possibility, is modified due to the non commutativity of spatial coordinates.
Rastall's theory is a generalization of Einstein's equations in which the energy-momentum tensor is not a conserved quantity, its covariant derivative is proportional to the gradient of the Ricci scalar and this fact can be associated with quantum effects in curved space-time. In this work we will go study the Rastall's gravity in the context of the Gödel-type universe.
In this article 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.
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
In this paper we investigate gravitational perturbations of a regular black hole, particularly Bardeen solution. Such system is solution of Einstein equations that do not have a singularity at the origin of the radial symmetry. However it still have events horizons depending on the values of the characteristic parameters of the solution. When a black hole is perturbed, it oscillates. It gives rise to damped vibrating modes which are known as quasinormal modes. It is calculated the quasinormal frequencies of a regular black hole using the third order WKB approximation for gravitational perturbations. The results are presented in tables I, II and III.
Using elements of symmetry, we constructed the Noncommutative Schrödinger Equation from a representation of Exotic Galilei Group. As consequence, we derive the Ehrenfest theorem using noncommutative coordinates. We also have showed others features of quantum mechanics in such a manifold. As an important result, we find out that a linear potential in the noncommutative Schrödinger equation is completely analogous to the ordinary case. We also worked with harmonic and anharmonic oscillators, giving corrections in the energy for each one.
This work is devoted to analyze the energy of the Universe in the context of f(T) theories. Such theories are the analogous counterpart of the well known f(R) theories that, however, uses torsion instead of curvature. We obtain a general expression for the gravitational energy-momentum vector in this framework. Using the hypothesis of the isotropy of spacetime, we find the energy of the Universe and compare it with the energy obtained in the realm of teleparallelism equivalent to general relativity (TEGR).
The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure, thus we use those expressions to construct the gravitational entropy. We interpret the cosmological constant as the temperature and write the first law of thermodynamics. In the limit $Λ\ll 1$ we find that the entropy is proportional to volume and $ΔS\geq 0$.
We show that plane-fronted gravitational waves induce the breaking of parallelograms in space-time, in the context of the teleparallel equivalent of general relativity (TEGR). The breaking of parallelograms can be shown by considering a thought experiment that consists of a simple physical configuration, similar to the experimental setup that is expected to lead to the measurement of gravitational waves with the use of laser interferometers. An incident beam of light splits into two beams running along perpendicular arms, endowed with fixed mirrors at the extremes. The reflected light beams are detected at the same point of the splitting. Along each arm, the two light beams define two null vectors: the forward vector and the reflected vector. We show that the sum of these four vectors, the forward and reflected null vectors along the two arms, do form a parallelogram in flat space-time, but not in the presence of plane-fronted gravitational waves. The non-closure of the parallelogram is a manifestation of the torsion of the space-time, and in this context indicates the existence of gravitational waves.
In this paper we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical simulations to find the relationship between the angular momentum of the field and the angular momentum of the source. Such a relation was established for each stable star reached by the numerical simulation once the code is fed with an equation of state, the central energy density and the ratio between polar and equatorial radii. We also find a regime where linear relation between gravitational angular momentum and moment of inertia (as well as angular velocity of the fluid) is valid. We give the spatial distribution of the gravitational energy and show that it has a linear dependence with the squared angular velocity of the source.
In this paper we work in the context of Teleparallelism Equivalent to General Relativity (TEGR) in order to construct the energy-momentum flux for Gödel-type solutions of Einstein's equations. We use an stationary observer, which is settled by the tetrad choice, to obtain the gravitational pressure for each direction of space in cartesian coordinates. Then we write down the total pressure for each direction in terms of the pressure of the fluid, thus we are able to identify role of the gravitational pressure.
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schrödinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physical consistent theory in phase space is constructed. The state is described by a quasi-probability amplitude that is in association with the Wigner function. The 3D harmonic oscillator and the noncommutative oscillator are studied in phase space as an application, and the Wigner function associated to both cases are determined.
In this work we use the theory of Teleparallelism Equivalent to General Relativity based in non-commutative space-time coordinates. In this context, we write the corrections of the Schwarzschild solution. As a important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the non-commutativity of space-time. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.
The concept of gravitational pressure is naturally defined in the context of the teleparallel equivalent of general relativity. Together with the definition of gravitational energy, we investigate the thermodynamics of rotating black holes in the teleparallel framework. We obtain the value of the gravitational pressure over the external event horizon of the Kerr black hole, and write an expression for the thermodynamic relation $TdS =dE + pdV$, where the variations refer to the Penrose process for the Kerr black hole. We employ only the notions of gravitational energy and pressure that arise in teleparallel gravity, and do not make any consideration of the area or the variation of the area of the event horizon. However, our results are qualitatively similar to the standard expression of the literature.
We investigate the gravitational energy-momentum distribution in the space-time of two black holes in circular orbit, in the context of the teleparallel equivalent of general relativity. This field configuration is important because gravitational waves are expected to be emitted in the final stages of inspiral and merger of binary black holes. We address an approximate solution of Einstein's field equations that describes two non-spinning black holes that circle each other in the $xy$ plane, obtain the total energy of the space-time and verify that the gravitational binding energy is negative. We show that gravitational radiation is emitted as long as the separation between the holes decreases in time. If the black holes are spinning and circle each other, it has been found in the literature that, during the pre-merger inspiral, they bob up and down sinusoidally. The understanding of this phenomenon requires the understanding of the gravitational energy-momentum flow in the space-time of binary black holes. For the time dependent metric tensor of a general binary black hole system, the non-vanishing of the gravitational momentum may explain the bobbing of spinning black holes.