arXiv subjects

A. F. F. Teixeira

Publications and source records attributed to A. F. F. Teixeira.

At least 37 records · Page 2Linked to original sources

arXiv2003

Movoj sub newtona logaritma potencialo

A linear density of mass is assumed uniformly distributed along an infinitely long straight line. All possible motions of a test particle are described, under the newtonian logarithmic gravitational potential alone. Those most interesting occur in planes normal to the line. An infinity of closed orbits are found, and classified in terms of two positive integers. ----- Maso kun uniforma linia denseco estas ordata sur nefinita rekto. /Gi produktas newtona logaritma potencialo. /Ciu ebla movo de test-parteto estas studata. La plej interesaj movoj okazas en plano normala al linio de maso. Nefinita qvanto de fermaj trajektorioj estas findataj, kaj klasifikataj per du pozitivaj entjeroj.

physics.class-ph↗

arXiv2002

Spikes in Cosmic Crystallography

If the universe is multiply connected and small the sky shows multiple images of cosmic objects, correlated by the covering group of the 3-manifold used to model it. These correlations were originally thought to manifest as spikes in pair separation histograms (PSH) built from suitable catalogues. Using probability theory we derive an expression for the expected pair separation histogram (EPSH) in a rather general topological-geometrical-observational setting. As a major consequence we show that the spikes of topological origin in PSH's are due to translations, whereas other isometries manifest as tiny deformations of the PSH corresponding to the simply connected case. This result holds for all Robertson-Walker spacetimes and gives rise to two basic corollaries: (i) that PSH's of Euclidean manifolds that have the same translations in their covering groups exhibit identical spike spectra of topological origin, making clear that even if the universe is flat the topological spikes alone are not sufficient for determining its topology; and (ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological origin. These corollaries ensure that cosmic crystallography, as originally formulated, is not a conclusive method for unveiling the shape of the universe. We also present a method that reduces the statistical fluctuations in PSH's built from simulated catalogues.

gr-qc↗

arXiv2001

Separations inside a cube

Two points are randomly selected inside a three-dimensional euclidian cube. The value l of their separation lies somewhere between zero and the length of a diagonal of the cube. The probability density P(l) of the separation is obtained analytically. Also a Monte Carlo computer simulation is performed, showing good agreement with the formulas obtained.

math.GM↗

arXiv2001

Distances in plane membranes

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is developed, and is easily extended to spaces with more dimensions.

physics.bio-ph↗

arXiv2001

On the interpretation of cylindrically symmetric Levi-Civita spacetime for 0<sigma<infinity

We study Levi-Civita metric for values of its sigma parameter in the range 0< sigma<infinity. We show that the value sigma=1/2 makes the axial and angular coordinates switch meaning. We present its geodesics and a physical source satisfying the energy conditions for all the range of sigma. This source allows us to obtain an energy per unit length which agrees with the behaviour of the geodesics and the fact that the solution has no event horizon.

gr-qc↗

arXiv2001

Signature for the Shape of the Universe

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson-Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.

gr-qc↗

arXiv2001

A Topological Signature in Cosmic Topology

Two procedures for obtaining (extracting and constructing) the topological signature of any multiply connected Robertson-Walker (RW) universe are presented. It is shown through computer-aided simulations that both approaches give rise to the same topological signature for a multiply connected flat RW universe. The strength of these approaches is illustrated by extracting the topological signatures of a flat ($k=0$), an elliptic ($k=1$), and a hyperbolic ($k=-1$) multiply connected RW universes. We also show how separated contributions of the covering isometries add up to form the topological signature of a RW flat universe. There emerges from our theoretical results and simulations that the topological signature arises (in the mean) even when there are just a few images for each object. It is also shown that the mean pair separation histogram technique works, and that it is a suitable approach for studying the topological signatures of RW universes as well as the role of non-translational isometries.

gr-qc↗

arXiv2000

Cosmic crystallography: the hyperbolic isometries

All orientation preserving isometries of the hyperbolic three-space are studied, and the probability density of conjugate pair separations for each isometry is presented. The study is relevant for the cosmic crystallography, and is the theoretical counterpart of the mean histograms arising from computer simulations of the isometries.

gr-qc↗

arXiv2000

Cosmic crystallography in a circle

In a circle (an S^1) with circumference 1 assume m objects distributed pseudo-randomly. In the universal covering R^1 assume the objects replicated accordingly, and take an interval L>1. In this interval, make the normalized histogram of the pair separations which are not an integer. The theoretical (expected) such histogram is obtained in this report, as well as its difference to a similar histogram for non-replicated objects. The whole study is of interest for the cosmic crystallography.

gr-qc↗

arXiv2000

Topological Reverberations in Flat Space-times

We study the role played by multiply-connectedness in the time evolution of the energy E(t) of a radiating system that lies in static flat space-time manifolds M_4 whose t=const spacelike sections M_3 are compact in at least one spatial direction. The radiation reaction equation of the radiating source is derived for the case where M_3 has any non-trivial flat topology, and an exact solution is obtained. We also show that when the spacelike sections are multiply-connected flat 3-manifolds the energy E(t) exhibits a reverberation pattern with discontinuities in the derivative of E(t) and a set of relative minima and maxima, followed by a growth of E(t). It emerges from this result that the compactness in at least one spatial direction of Minkowski space-time is sufficient to induce this type of topological reverberation, making clear that our radiating system is topologically fragile. An explicit solution of the radiation reaction equation for the case where M_3 = R^2 x S^1 is discussed, and graphs which reveal how the energy varies with the time are presented and analyzed.

gr-qc↗

arXiv2000

Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSH's using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSH's corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.

gr-qc↗

arXiv2000

Cosmic crystallography: the euclidean isometries

Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of the isometries. For completeness, also the isometries with fixed points are examined, as well as the orientation reversing isometries.

gr-qc↗

arXiv1999

Gödel-type Spacetimes in Induced Matter Gravity Theory

A five-dimensional (5D) generalized Gödel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters $k$, $m^2$ and $ω$: identical triads $(k, m^2, ω)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized Gödel-type 5D manifolds admit maximal group of isometry $G_r$ with $r=7$, $r=9$ or $r=15$ depending on the essential parameters $k$, $m^2$ and $ω$. The breakdown of causality in all these classes of homogeneous Gödel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized Gödel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these type of causal anomalies of general relativity is also discussed in connection with a recent article by Romero, Tavakol and Zalaletdinov.

gr-qc↗

arXiv1999

Cosmic crystallography: three multi-purpose functions

A solid sphere is considered, with a uniformly distributed infinity of points. Two points being pseudorandomly chosen, the analytical probability density that their separation have a given value is computed, for three types of the underlying geometry: $E^3, H^3$ and $S^3$. Figures, graphs and histograms to complement this short note are given.

astro-ph↗

arXiv1998

Causal Anomalies in Kaluza-Klein Gravity Theories

Causal anomalies in two Kaluza-Klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. It is found that similarly to general relativity the field equations of the space-time-mass Kaluza-Klein (STM-KK) gravity theory do not exclude violation of causality of Gödel type, whereas the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal Gödel-type models. The induced matter version of general relativity is shown to be an efficient therapy for causal anomalies that occurs in a wide class of noncausal geometries. Perfect fluid and dust Gödel-type solutions of the STM-KK field equations are studied. It is shown that every Gödel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5-D Gödel-type non-causal geometries induce any physically acceptable 4-D energy-momentum tensor is also addressed.

gr-qc↗

arXiv1998

Radiation Damping in FRW Space-times with Different Topologies

We study the role played by the compactness and the degree of connectedness in the time evolution of the energy of a radiating system in the Friedmann-Robertson-Walker (FRW) space-times whose $t=const $ spacelike sections are the Euclidean 3-manifold ${\cal R}^3$ and six topologically non-equivalent flat orientable compact multiply connected Riemannian 3-manifolds. An exponential damping of the energy $E(t)$ is present in the ${\cal R}^3$ case, whereas for the six compact flat 3-spaces it is found basically the same pattern for the evolution of the energy, namely relative minima and maxima occurring at different times (depending on the degree of connectedness) followed by a growth of $E(t)$. Likely reasons for this divergent behavior of $E(t)$ in these compact flat 3-manifolds are discussed and further developments are indicated. A misinterpretation of Wolf's results regarding one of the six orientable compact flat 3-manifolds is also indicated and rectified.

gr-qc↗

arXiv1997

Riemannian Space-times of Gödel Type in Five Dimensions

The five-dimensional (5D) Riemannian Gödel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by two essential parameters $m^2$ and $ω$: identical pairs $(m^2, ω)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that apart from the $(m^2= 4 ω^2, ω\not=0)$ and $(m^2\not=0, ω= 0)$ classes the homogeneous Riemannian Gödel-type manifolds admit a seven-parameter maximal group of isometry ($G_7$). The special class $(m^2= 4 ω^2, ω\not=0)$ and the degenerated Gödel-type class $(m^2\not=0, ω=0)$ are shown to have a $G_9$ as maximal group of motion. The breakdown of causality in these classes of homogeneous Gödel-type manifolds are also examined.

gr-qc↗

arXiv1997

Topology and Fragility in Cosmology

We introduce the notion of topological fragility and briefly discuss some examples from the literature. An important example of this type of fragility is the way globally anisotropic Bianchi V generalisations of the FLRW $k=-1$ model result in a radical restriction on the allowed topology of spatial sections, thereby excluding compact cosmological models with negatively curved three-sections with anisotropy. An outcome of this is to exclude chaotic mixing in such models, which may be relevant, given the many recent attempts at employing compact FLRW $k=-1$ models to produce chaotic mixing in the cosmic microwave background radiation, if the Universe turns out to be globally anisotropic.

gr-qc↗