arXiv subjects

Ion I. Cotaescu

Publications and source records attributed to Ion I. Cotaescu.

At least 55 records · Page 3Linked to original sources

arXiv2017

Anti-de Sitter relativity

The relative geodesic motion on $(1+3)$-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the Lorentzian isometriy is derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive mobile object moving on a timelike anti-de Sitter geodesic. The transformation of the conserved quantities is also investigated, constructing thus a complete theory of the relative geodesic motion on anti-de Sitter spacetimes. Some applications are discussed among them the problems of twin paradox and Lorentz contraction are solved.

gr-qc↗

arXiv2017

Rest frames and relativistic effects on de Sitter spacetimes

It is shown that the Nachtmann boosting method of introducing coordinates on de Siter manifolds can be completed with suitable gauge transformations able to keep under control the transformation under isometries of the conserved quantities. With this method, the rest local charts (or natural frames) are defined pointing out the role of the conserved quantities in investigating the relative geodesic motion. The advantages of this approach can be seen from the applications presented here. For the first time, the simple kinematic effects, the electromagnetic field of a free falling charge and the binary fission are solved in terms of conserved quantities on the expanding portion of the de Sitter spacetime.

gr-qc↗

arXiv2017

Physical meaning of the conserved quantities on anti-de Sitter geodesics

The geodesic motion on anti-de Sitter spacetimes is studied pointing out how the trajectories are determined by the ten independent conserved quantities associated to the specific SO(2,3) isometries of these manifolds. The new result is that there are two conserved SO(3) vectors which play the same role as the Runge-Lenz vector of the Kepler problem, determining the major and minor semiaxes of the ellipsoidal anti-de Sitter geodesics.

gr-qc↗

arXiv2017

Relative motion and rest frames on de Sitter spacetimes

The Nachtmann boosting method is completed with gauge transformations in order to be applied to the study of the relative geodesic motion on the de Sitter spacetimes, finding how the conserved quantities transform under isometries and defining the rest frames of massive mobiles.

gr-qc↗

arXiv2016

On the de Sitter Tardyons and Tachyons

It is shown that on the de Sitter manifolds the tachyonic geodesics are restricted such that the classical tachyons cannot exist on this manifold at any time. On the contrary, the theory of the scalar quantum tachyons is free of any restriction. The tachyonic scalar and Dirac plane waves are deduced in this geometry, pointing out that these are well-defined, behaving as tempered distributions at any moment.

gr-qc↗

arXiv2016

Relativistic persistent currents in ideal Aharonov-Bohm rings and cylinders

The exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents at $T=0$ is evaluated for rings and cylinders obtaining approximative simple closed formulas.

quant-ph↗

arXiv2016

Maxwell-Juttner distribution for rigidly-rotating flows in spherically symmetric spacetimes using the tetrad formalism

We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.

hep-th↗

arXiv2016

Partial wave analysis of the Dirac fermions scattered from Reissner - Nordstr\" om charged black holes

The asymptotic form of Dirac spinors in the field of the Reissner-Nordstrom black hole are derived for the scattering states (with $E>mc^2$) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. The elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analysing the differential cross section (forward/backward scattering) and the polarization degree as functions of scattering angle.

gr-qc↗

arXiv2016

Elements of Linear Algebra. Lecture Notes

These pedagogical lecture notes address to the students in theoretical physics for helping them to understand the mechanisms of the linear operators defined on finite-dimensional vector spaces equipped with definite or indefinite inner products. The importance of the Dirac conjugation is pointed out presenting its general theory and a version of the Riesz theorem for the indefinite inner product spaces, based on the Dirac-Riesz map that combines the action of the Riesz map with that of the metric operator. The matrix representations of the linear operators on vector spaces with definite or indefinite inner products is also presented.

math.HO↗

arXiv2015

Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime

In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the $Sp(2,2)$ group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to a UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i. e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli-Lubanski type operator are also pointed out.

gr-qc↗

arXiv2015

Relativistic currents on ideal Aharonov-Bohm cylinders

The relativistic theory of the Dirac fermions moving on cylinders in external Aharonov-Bohm field is built starting with a suitably restricted Dirac equation whose spin degrees of freedom are not affected. The exact solutions of this equation on finite or infinite Aharonov-Bohm cylinders allow one to derive the relativistic circular and longitudinal currents pointing out their principal features. It is shown that all the circular currents are related to the energy in the same manner on cylinders or rings either in the relativistic approach or in the non-relativistic one. The specific relativistic effect is the saturation of the circular currents for high values of the total angular momentum. Based on this property some approximative closed formulas are deduced for the total persistent current at $T=0$ on finite Aharonov-Bohm cylinders. Moreover, it is shown that all the persistent currents on finite cylinders or rings have similar non-relativistic limits.

quant-ph↗

arXiv2015

Relativistic persistent currents in ideal Aharonov-Bohm rings

The exact solutions of the complete Dirac equation for fermions moving in ideal Aharonov-Bohm rings are used for deriving the exact expressions of the relativistic partial currents. It is show that as in the non-relativistic case these currents can be related to the derivative of the fermion energy with respect to the flux parameter. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent current at $T=0$ is evaluated giving its analytical expression and showing how this depend on the ring parameters.

quant-ph↗

arXiv2015

Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes

Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, $E>mc^2$) in Schwarzschild's chart and Cartesian gauge, are used for building the partial wave analysis of Dirac fermions scattered by black holes. The contribution of the bound states to absorption and possible resonant scattering is neglected because of some technical difficulties related to the discrete spectrum that is less studied so far. In this framework, the analytic expressions of the differential cross section and induced polarization degree are derived in terms of scattering angle, mass of the black hole, energy and mass of the fermion. Moreover, the closed form of the absorption cross section due to the scattering modes is derived showing that in the high-energy limit this tends to the event horizon area regardless of the fermion mass (including zero). A graphical study presents the differential cross section analyzing the forward/backward scattering (known also as glory scattering) and the polarization degree as functions of scattering angle. The graphical analysis shows the presence of oscillations in scattering intensity around forward/backward directions, phenomena known as spiral scattering. The energy dependence of the differential cross section is also established by using analytical and graphical methods.

gr-qc↗

arXiv2015

Acceleration in de Sitter spacetimes

We propose a definition of uniform accelerated frames in de Sitter spacetimes applying the Nachtmann method of introducing coordinates using suitable point-dependent isometries. In order to recover the well-known Rindler approach in the flat limit, we require the transformation between the static frame and the accelerated one to depend continuously on acceleration, obtaining thus the natural generalization of the Rindler transformation to the de Sitter spacetimes of any dimensions.

gr-qc↗

arXiv2014

On anti-de Sitter oscillators and de Sitter anti-oscillators

We revisit the principal arguments for interpreting the free quantum fields on anti-de Sitter or de Sitter spacetimes of any dimensions as oscillators or respectively anti-oscillators. In addition, we point out that there exists a chart on the de Sitter background where the free Dirac field becomes a genuine anti-oscillator in the non-relativistic limit in the sense of special relativity.

gr-qc↗

arXiv2014

Accelerated frames in de Sitter spacetime

We propose a definition of the accelerated frames in de Sitter spacetime whose metric recovers the Rindler approach in the flat limit. Unfortunately, this metric has no a satisfactory limit for vanishing acceleration such that its physical meaning remains obscure.

gr-qc↗

arXiv2014

Discrete symmetries determining scalar quantum modes on the de Sitter spacetime

The action of the discrete symmetries on the scalar mode functions of the de Sitter spacetime is studied. The invariance with respect to a combination of discrete symmetries is put forward as a criterion to select a certain vacuum out of a family of vacua. The implications of the choices for eigenfunctions of various common sets of commuting operators are explored, and the results are compared to the different original choices from the literature that have been utilized in order to exhibit thermal effects.

gr-qc↗

arXiv2013

On the rest and flat limits of the scalar modes on the de Sitter spacetime

The scalar mode functions on the spatially flat FLRW chart of the de Sitter spacetime are redefined in order to obtain a natural frequencies separation in the special local charts where the momentum vanishes, called here (natural) rest frames. This can be done since in such frames the mode functions are eigenfunctions of the energy operator. Moreover, the most general criteria for choosing the suitable phase factors of the mode functions able to simultaneously determine the correct rest and flat limits are established. These results are compared to the different original choices from the literature. Pacs: 04.62.+v

gr-qc↗