arXiv subjects

N. A. Lemos

Publications and source records attributed to N. A. Lemos.

16 recordsLinked to original sources

arXiv2024

Gödel-type spacetimes in $f(Q)$ gravity

There is ongoing interest in the nonmetricity formulation of gravity. The nonlinear extension of the theory, called $f(Q)$ gravity, has recently been proposed and offers a promising avenue for addressing some of the long-standing challenges in cosmology and fundamental physics. A number of solutions have already been found that have confirmed the usefulness of the theory for astrophysics and cosmology. Motivated by earlier work on Gödel-type spacetimes we investigate whether $f(Q)$ gravity admits such cosmological solutions, which entail causality violation. In the coincident gauge, which is shown to be a legitimate gauge because the connection field equations are satisfied, we find that Gödel-type metrics are allowed by this modified gravity theory for any function $f(Q)$. Noncausal and causal solutions exist depending on the matter content. For a perfect fluid, out of all Gödel-type metrics only Gödel's original model is allowed in $f(Q)$ gravity, implying violation of causality. The requirement that energy conditions be obeyed by the fluid leads to mild restrictions on $f(Q)$. For a massless scalar field in the presence of a cosmological constant, there are causal solutions for any reasonable function $f(Q)$.

gr-qc↗

arXiv2023

Probing time orientability of spacetime

In general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics require these orientability assumptions is ultimately of observational or experimental nature, or the answer might come from a fundamental theory of physics. The possibility that spacetime is time non-orientable lacks investigation, and so should not be dismissed straightaway. In this paper, we argue that it is possible to locally access a putative time non-orientability of Minkowski empty spacetime by physical effects involving quantum vacuum electromagnetic fluctuations. We set ourselves to study the influence of time non-orientability on the stochastic motions of a charged particle subject to these electromagnetic fluctuations in Minkowski spacetime equipped with a time non-orientable topology and with its time orientable counterpart. To this end, we introduce and derive analytic expressions for a statistical time orientability indicator. Then we show that it is possible to pinpoint the time non-orientable topology through an inversion pattern displayed by the corresponding orientability indicator, which is absent when the underlying manifold is time orientable.

gr-qc↗

arXiv2022

Probing spatial orientability of Friedmann--Robertson--Walker spatially flat spacetime

One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a non-orientable spacetime is another theoretical argument for orientability. However, it is conceivable that orientability can be put to test by local physical effects. In this paper, we show that it is possible to locally access spatial orientability of a spatially flat Friedmann--Robertson-Walker spacetime through quantum vacuum electromagnestic fluctuations. We argue that a putative non-orientability of the spatial sections of spatially flat FRW spacetime can be ascertained by the study of the stochastic motions of a charged particle or a point electric dipole under quantum vacuum electromagnetic fluctuations. In particular, the stochastic motions of a dipole permit the recognition of a presumed non-orientability of $3-$space in itself.

gr-qc↗

arXiv2021

Orientability of space from electromagnetic quantum fluctuations

Whether the space where we live is a globally orientable manifold $M_3$, and whether the local laws of physics require that $M_3$ be equipped with a canonical orientation, are among the unsettled questions in cosmology and quantum field theory. It is often assumed that a test for spatial orientability requires a global journey across the whole $3-$space. Since such a global expedition is not feasible, theoretical arguments are usually offered to support the choice of time orientation for the spacetime manifold $M_4$, and space orientation for $M_3$. Theoretical arguments can certainly be used, but one would expect that the ultimate answer to the orientability question should rely on observations or local experiments, or can come from a topological fundamental theory in physics. In a recent paper we have argued that it is potentially possible to locally access the $3-$space orientability of Minkowski spacetime through effects involving 'point-like charged particles' under quantum electromagnetic fluctuations. Specifically, we studied the stochastic motions of a charged particle and an electric dipole subjected to these fluctuations in Minkowski spacetime, with either an orientable or a non-orientable $3-$space topology, and derived expressions for a statistical orientability indicator in these two flat topologically inequivalent manifolds. For the dipole we found that a characteristic inversion pattern exhibited by the curves of the orientability indicator is a signature of non-orientability, making it possible to locally probe the orientability of the $3-$space. Here, to shed some additional light on the spatial orientability, we briefly review these results, and also discuss some of its features and consequences. The results might open the way to a conceivable experiment involving quantum fluctuations to look into the spatial orientability of Minkowski empty spacetime.

gr-qc↗

arXiv2021

Inquiring electromagnetic quantum fluctuations about the orientability of space

Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial orientability requires a journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are offered to support the choosing of time- and space-orientable spacetime manifolds. We show that it is possible to access spatial orientability of Minkowski spacetime through local physical effects involving quantum electromagnetic fluctuations. To this end, we study the motions of a charged particle and an electric dipole under these fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive expressions for an orientability indicator for both point-like particles in two spatially flat topologies. For the particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the evolution of the indicators. This shows that it is possible to access orientability through electromagnetic quantum fluctuations.The answer to the question on how to locally probe the orientability of Minkowski 3-space intrinsically arises in the study of the dipole's motions. We find that a characteristic inversion pattern exhibited by the dipole indicator curves is a signature of non-orientability. This result makes it clear that it is possible to locally unveil spatial non-orientability by the inversion pattern of orientability indicator curves of an electric dipole under electromagnetic fluctuations. Our findings open the way to a conceivable experiment involving quantum electromagnetic fluctuations to locally probe the spatial orientability on the microscopic scale of Minkowski spacetime.

hep-th↗

arXiv2016

Kelvin transformation and inverse multipoles in electrostatics

The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are obtained through the mapping from simple highly symmetric systems. In particular, the concept of multipole expansion is revisited from a point of view opposed to the usual one: the sources are distributed in a region far from the origin while the electrostatic potential is described at points close to it.

physics.class-ph↗

arXiv2010

Probing singularities in quantum cosmology with curvature scalars

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.

gr-qc↗

arXiv2007

Reply to "Comment on 'Quantization of FRW spacetimes in the presence of a cosmological constant and radiation'"

The Comment by Amore {\it et al.} [gr-qc/0611029] contains a valid criticism of the numerical precision of the results reported in a recent paper of ours [Phys. Rev. D {\bf 73}, 044022 (2006)], as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.

gr-qc↗

arXiv2005

Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

We quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or zero. They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schroedinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev, and use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expected value of the scale factors. We find for all of them that the expected values of the scale factors oscillate between maximum and minimum values. Since the expectation values of the scale factors never vanish, we conclude that these models do not have singularities.

gr-qc↗

arXiv2002

A Quantum Cosmological Model With Static and Dynamic Wormholes

Quantization is performed of a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state $p=αρ$. A well-known discrete set of static quantum wormholes is shown to exist for radiation ($α=1/3$), and a novel continuous set is found for cosmic strings ($α= -1/3$), the latter states having throat radii of any size. In both cases wave-packet solutions to the Wheeler-DeWitt equation are obtained with all the properties of evolving quantum wormholes. In the case of a radiation fluid, a detailed analysis of the quantum dynamics is made in the context of the Bohm-de Broglie interpretation. It is shown that a repulsive quantum force inversely proportional to the cube of the scale factor prevents singularities in the quantum domain. For the states considered, there are no particle horizons either.

gr-qc↗

arXiv2002

A dipole in a dielectric: Intriguing results and shape dependence of the distant electric field

The field of a point electric dipole in an infinite dielectric is obtained by placing the dipole at the center of a spherical cavity of radius $R$ inside the dielectric and then letting $R\to 0$. The result disagrees with the elementary answer found in textbooks. The mathematical and physical reasons for the disagreement are discussed. The discrepancy is confirmed by the same limiting procedure applied to a uniformly polarized sphere embedded in the dielectric. We next solve the same problem for a polarized spheroid immersed in an infinite dielectric and find that the asymptotic potential shows an unexpected shape dependence, even after taking the limit of an arbitrarily small spheroid. By considering both oblate and prolate spheroids and taking appropriate limits, we recover either the elementary textbook answer or the previous result found for the polarized sphere.

physics.class-ph↗

arXiv2002

Quantum cosmological perfect fluid models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = αρ$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $α< 1$. Accelerated expansion at present requires $- 1/3 > α> - 1$.

gr-qc↗

arXiv1998

Higher-Derivative Two-Dimensional Massive Fermion Theories

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N+1 consist of a physical usual massive fermion, quantized with positive metric, plus 2N unphysical massless fermions, quantized with opposite metrics. The positive metric Hilbert subspace, which is isomorphic to the space of states of a massive free fermion theory, is selected by a subsidiary-like condition. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used as a guideline to discuss the solution of a theory including a current-current interaction.

hep-th↗

arXiv1998

Structural Aspects of Two-Dimensional Anomalous Gauge Theories

A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the fundamental set of field operators whose Wightman functions define the model. We examine the effect of the use of a redundant field algebra in deriving basic properties of the models and show that different results may arise, as regards the physical properties of the generalized chiral model, in restricting or not the Hilbert space as representation of the intrinsic local field algebra. The question referring to considering the vector Schwinger model as a limit of the generalized anomalous model is also discussed. We show that this limit can only be consistently defined for a field subalgebra of the generalized model.

hep-th↗

arXiv1997

Higher-Derivative Massive Fermion Theories

We propose and canonically quantize a generalization of the two-dimensional massive fermion theory described by a Lagrangian containing third-order derivatives. In our approach the mass term contains a derivative coupling. The quantum solution is expressed in terms of three usual fermions. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used to solve a theory including a current-current interaction.

hep-th↗

arXiv1995

Canonical Transformations in a Higher-Derivative Field Theory

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiral-gauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.

hep-th↗