Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Bringing together gravity and the quanta

Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacement of general relativity by its teleparallel equivalent can be considered an important step towards a prospective reconciliation between gravitation and quantum mechanics. © 2006 American Institute of Physics.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

Some implications of the cosmological constant to fundamental physics

In the presence of a cosmological constant, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the ordinary notions of energy and momentum change, and will satisfy a different kinematic relation. Such a theory is a different kind of a doubly special relativity. Since the only difference between the Poincaré and the de Sitter groups is the replacement of translations by certain linear combinations of translations and proper conformal transformations, the net result of this change is ultimately the breakdown of ordinary translational invariance. From the experimental point of view, therefore, a de Sitter special relativity might be probed by looking for possible violations of translational invariance. If we assume the existence of a connection between the energy scale of an experiment and the local value of the cosmological constant, there would be changes in the kinematics of massive particles which could hopefully be detected in high-energy experiments. Furthermore, due to the presence of a horizon, the usual causal structure of spacetime would be significantly modified at the Planck scale. © 2007 American Institute of Physics.

Gravitation: In search of the missing torsion

A linear Lorentz connection has always two fundamental derived characteristics: curvature and torsion. The latter is assumed to vanish in general relativity. Three gravitational models involving non-vanishing torsion are examined: teleparallel gravity, Einstein-Cartan, and new general relativity. Their dependability is critically examined. Although a final answer can only be given by experience, it is argued that teleparallel gravity provides the most consistent approach.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

On the consistency conditions to braneworlds in scalar-tensor gravity for arbitrary dimensions

We derive an one-parameter family of consistency conditions to braneworlds in the Brans-Dicke gravity. The General Relativity case is recovered by taking a correct limit of the Brans-Dicke parameter. We show that it is possible to build a multiple AdS brane scenario in a six-dimensional bulk only if the brane tensions are negative. Besides, in the five-dimensional case, it is showed that no fine tuning is necessary between the bulk cosmological constant and the brane tensions, in contrast to the Randall-Sundrum model. Copyright © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial- ShareAlike Licence.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

Sending classical information through relativistic quantum channels

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps. © 2013 American Physical Society.

Scaling attractors in interacting teleparallel dark energy

It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found. Here we consider a model in which the non-minimal coupling is ruled by a dynamically changing coefficient α≡f,φ/(f)1/2, with f(φ) an arbitrary function of the scalar field φ. It is shown that in this case the existence of scaling attractors is possible, which means that the universe will eventually enter these scaling attractors, regardless of the initial conditions. As a consequence, the cosmological coincidence problem could be alleviated without fine-tunings. © 2013 IOP Publishing Ltd and Sissa Medialab srl.

Posicionamento por ponto preciso estático e cinemático: implementação e análise

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ensaio sobre o fluxo de Ricci e os buracos negros: fundamentação e estudo computacional

Pós-graduação em Ciência da Computação - IBILCE

Relatividade restrita de De Sitter: uma abordagem cinemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Deflexão de fótons pelo sol no contexto da teoria de gravitação R+R2

Pós-graduação em Física - IFT