The hybrid metric-Palatini \(f({\mathscr {R}})\) gravity is a recently devised approach to modified gravity in which it is added to the metric Ricci scalar R, in the Einstein–Hilbert Lagrangian, a function \(f({\mathscr {R}})\) of Palatini curvature scalar \({\mathscr {R}}\), which is constructed from an independent connection. These hybrid metric-Palatini gravity theories provide an alternative way to explain the current accelerating expansion without a dark energy matter component. If gravitation is to be described by a hybrid metric-Palatini \(f({\mathscr {R}})\) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of \(f({\mathscr {R}})\) theories, we examine whether they admit Gödel-type solutions for physically well-motivated matter source. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous (ST-homogeneous) solutions in \(f({\mathscr {R}})\) theories reduces to the problem of determining solutions of Einstein’s field equations with a cosmological constant. Employing this far-reaching result, we determine a general ST-homogeneous Gödel-type solution whose matter source is a combination of a scalar with an electromagnetic fields plus a perfect fluid. This general Gödel-type solution contains special solutions in which the essential parameter \(m^2\) can be \(m^{2} > 0\) hyperbolic family, \(m=0\) linear class, and \(m^{2} < 0\) trigonometric family, covering thus all classes of homogeneous Gödel-type spacetimes. This general solution also contains all previously known solutions as special cases. The bare existence of these Gödel-type solutions makes apparent that hybrid metric-Palatini \(f({\mathscr {R}})\) gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity.

La transformoj de Schwarz-Christoffel mapas, konforme, la superan kompleksan duon-ebenon al regiono limigita per rektaj segmentoj. Cxi tie ni priskribas kiel konvene kunigi mapon de la suba duon-ebeno al mapo de la supera duon-ebeno. Ni emfazas la bezonon de klara difino de angulo de kompleksa nombro, por tiu kunigo. Ni diskutas kelkajn ekzemplojn kaj donas interesan aplikon pri movado de fluido. ------- Schwarz-Christoffel transformations map, conformally, the complex upper half plane into a region bounded by right segments. Here we describe how to couple conveniently a map of the lower half plane to the map of the upper half plane. We emphasize the need of a clear definition of angle of a complex, to that coupling. We discuss some examples and give an interesting application for motion of fluid.

The \(f(R)\) gravity theories provide an alternative way to explain the current cosmic acceleration without invoking a dark energy matter component used in the cosmological modeling in the framework of general relativity. However, the freedom in the choice of the functional forms of \(f(R)\) gives rise to the problem of the degeneracy among these gravity theories on theoretical and (or) observational grounds. In this paper we examine the question as to whether the future dynamics can be used to break the degeneracy between \(f(R)\) gravity theories by investigating the dynamics of spatially homogeneous and isotropic dust flat models in two \(f(R)\) gravity theories, namely the well-known \(f(R) = R + \alpha R^{n}\) gravity and another by Aviles et al., whose motivation comes from the cosmographic approach to \(f(R)\) gravity. We perform a detailed numerical study of the dynamics of these theories taking into account the recent constraints on the cosmological parameters made by the Planck Collaboration. We demonstrate that besides being useful for discriminating between these two \(f(R)\) gravity theories, the future dynamics technique can also be used to determine the finite-time behavior as well as the fate of the Universe in the framework of these \(f(R)\) gravity theories. There also emerges from our analysis the result that one still can have a dust flat FLRW solution with a big rip, if gravity is governed by \(f(R) = R + \alpha R^n \). We also show that FLRW dust solutions with \(f''<0\) do not necessarily lead to singularities.

In the special relativity, a rigid rod slides upon itself, with one extremity oscillating harmonically. We discovered restrictions in the amplitude of the motion and in the length of the rod, essential to eliminate unphysical solutions. ------- Cxe la speciala relativeco, rigida stango movigxas sur si mem, kun unu fino oscilante harmonie. Ni malkovris limigajn kondicxojn pri la amplitudo de movado kaj pri la longo de stango, necesegaj por elimini ne-fizikajn solvojn.

Despite our present-day inability to predict the topology of the universe it is expected that we should be able to detect it in the near future. A nontrivial detectable topology of the space section of the universe can be probed for all homogeneous and isotropic universes through the circles-in-the-sky. We discuss briefly how one can use this observable attribute to set constraints on the dark energy equation of state parameters.

The theory of relativity showed that several Newtonian ideas about spacetime are imperfect. We present here some relativistic concepts related to these ideas: simultaneity of events and synchronization of clocks (both along a line in the space frame), gravitational Doppler effect, and time travel. --------- La relativeca teorio montris ke pluraj Newtonaj ideoj pri la spacotempo estas malperfektaj. Tie cxi ni prezentas kelkajn relativecajn konceptojn iel rilatajn al tiuj ideoj: samtempecon de eventoj kaj sinkronon de horlogxoj (ambaux laux linio en la spaca reto), gravitan Doppleran efikon, kaj vojagxon kun reveno al estinto.

In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular motion with constant velocity, particularly closed timelike curves, and time travel of a voyager. ------------------- ^Ce la ^Generala Relativeco, en homogena metriko de Som-Raychaudhuri, ni studas geodeziojn de la tri tipoj: tempa, nula, kaj spaca, speciale la malmulte konatajn samtempajn geodeziojn. Ni anka^u studas ne-geodezian cirklan movadon kun konstanta rapido, speciale fermitajn kurbojn de tempa tipo, kaj movadon de voja^ganto al estinto.

In a $n$-dimensional Lie algebra, random numerical values are assigned by computer to $n(n-1)$ especially selected structure constants. An algorithm is then created, which calculates without ambiguity the remaining constants, obeying the Jacobi conditions. Differently from others, this algorithm is suitable even for poor personal computer. ------------- En $n$-dimensia algebro de Lie, hazardaj numeraj valoroj estas asignitaj per komputilo al $n(n-1)$ speciale elektitaj konstantoj de strukturo. Tiam algoritmo estas kreita, kalkulante senambigue la ceterajn konstantojn, obeante kondicxojn de Jacobi. Malsimile al aliaj algoritmoj, tiu cxi tauxgas ecx por malpotenca komputilo.

A detection or nondetection of primordial non-Gaussianity by using the cosmic microwave background radiation (CMB) offers a way of discriminating inflationary scenarios and testing alternative models of the early universe. This has motivated the considerable effort that has recently gone into the study of theoretical features of primordial non-Gaussianity and its detection in CMB data. Among such attempts to detect non-Gaussianity, there is a procedure that is based upon two indicators constructed from the skewness and kurtosis of large-angle patches of CMB maps, which have been proposed and used to study deviation from Gaussianity in the WMAP data. Simulated CMB maps equipped with realistic primordial non-Gaussianity are essential tools to test the viability of non-Gaussian indicators in practice, and also to understand the effect of systematics, foregrounds and other contaminants. In this work we extend and complement the results of our previous works by performing an analysis of non-Gaussianity of the high-angular resolution simulated CMB temperature maps endowed with non-Gaussianity of the local type, for which the level of non-Gaussianity is characterized by the dimensionless parameter f_ NL^ local

Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\mu}\dd x^\mu=0$). These geodesics are studied in the exterior region of \Sch's metric.

The detection of non-Gaussianity in the CMB data would rule out a number of inflationary models. A null detection of non-Gaussianity, instead, would exclude alternative models for the early universe. Thus, a detection or non-detection of primordial non-Gaussianity in the CMB data is crucial to discriminate among inflationary models, and to test alternative scenarios. However, there are various non-cosmological sources of non-Gaussianity. This makes important to employ different indicators in order to detect distinct forms of non-Gaussianity in CMB data. Recently, we proposed two new indicators to measure deviation from Gaussianity on large angular scales, and used them to study the Gaussianity of the raw band WMAP maps with and without the KQ75 mask. Here we extend this work by using these indicators to perform similar analyses of deviation from Gaussianity of the foreground-reduced Q, V, and W band maps. We show that there is a significant deviation from Gaussianity in the considered full-sky maps, which is reduced to a level consistent with Gaussianity when the KQ75 mask is employed.

Motion of bodies and light rays are studied in the gravitational field of Schwarzschild. Several Doppler effects are described. —– Movado de korpoj kaj lumo estas studitaj en gravita kampo de Schwarzschild. Pluraj Doppleraj efikoj estas priskribitaj.

A plane lights on monochromatically and immediately after lights off, while an observer starts moving out from the plane, perpendicularly to it, with constant proper acceleration. Special relativity predicts that the observer will see a light circle always in the direction opposite to the plane, without Doppler effect, and that the circle will seem to progressively shrink to a point. —– Ebeno eklumi^gas unukolore kaj tuj poste mallumi^gas, dum observanto ekmovi^gas orte el ebeno kun konstanta propra akcelo. Special-relativeco anta^udiras, ke observanto vidos luman cirklon ^ciam en direkto mala al la ebeno, sen Dopplera efiko, kaj ke tiu cirklo ^sajnos progrese eti^gi ^gis punkto.

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 constructed analytically. Also a Monte Carlo computer simulation is performed, showing good agreement with the formulas obtained.

We describe the Doppler effect between equally accelerated light source and observer under the special relativity. The proper accelerations are constant and parallel. An English version is available by request. - - - - - - - - - - - Ni priskribas luman Doppleran efikon inter same akcelataj fonto kaj observanto ^ce special-relativeco. La propraj akceloj estas konstantaj kaj paralelaj.

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. E-mail: german@cbpf.br E-mail: reboucas@cbpf.br E-mail: teixeira@cbpf.br