3 resultados para CLOSED TIMELIKE CURVES
em Universidade Federal do Rio Grande do Norte(UFRN)
Resumo:
In this dissertation, after a brief review on the Einstein s General Relativity Theory and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models, we present and discuss the alternative theories of gravity dubbed f(R) gravity. These theories come about when one substitute in the Einstein-Hilbert action the Ricci curvature R by some well behaved nonlinear function f(R). They provide an alternative way to explain the current cosmic acceleration with no need of invoking neither a dark energy component, nor the existence of extra spatial dimensions. In dealing with f(R) gravity, two different variational approaches may be followed, namely the metric and the Palatini formalisms, which lead to very different equations of motion. We briefly describe the metric formalism and then concentrate on the Palatini variational approach to the gravity action. We make a systematic and detailed derivation of the field equations for Palatini f(R) gravity, which generalize the Einsteins equations of General Relativity, and obtain also the generalized Friedmann equations, which can be used for cosmological tests. As an example, using recent compilations of type Ia Supernovae observations, we show how the f(R) = R − fi/Rn class of gravity theories explain the recent observed acceleration of the universe by placing reasonable constraints on the free parameters fi and n. We also examine the question as to whether Palatini f(R) gravity theories permit space-times in which causality, a fundamental issue in any physical theory [22], is violated. As is well known, in General Relativity there are solutions to the viii field equations that have causal anomalies in the form of closed time-like curves, the renowned Gödel model being the best known example of such a solution. Here we show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with density and pressure p that satisfy the weak energy condition + p 0 is necessarily isometric to the Gödel geometry, demonstrating, therefore, that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We derive an expression for a critical radius rc (beyond which causality is violated) for an arbitrary Palatini f(R) theory. The expression makes apparent that the violation of causality depends on the form of f(R) and on the matter content components. We concretely examine the Gödel-type perfect-fluid solutions in the f(R) = R−fi/Rn class of Palatini gravity theories, and show that for positive matter density and for fi and n in the range permitted by the observations, these theories do not admit the Gödel geometry as a perfect-fluid solution of its field equations. In this sense, f(R) gravity theory remedies the causal pathology in the form of closed timelike curves which is allowed in General Relativity. We also examine the violation of causality of Gödel-type by considering a single scalar field as the matter content. For this source, we show that Palatini f(R) gravity gives rise to a unique Gödeltype solution with no violation of causality. Finally, we show that by combining a perfect fluid plus a scalar field as sources of Gödel-type geometries, we obtain both solutions in the form of closed time-like curves, as well as solutions with no violation of causality
Resumo:
The system built to characterize electrodes and, consequently, deposited fine films are constituted by a hollow cathode that works to discharges and low pressures (approximately 10-3 to 5 mbar), a source DC (0 to 1200 V), a cylindrical camera of closed borossilicato for flanges of stainless steel with an association of vacuum bombs mechanical and spread. In the upper flange it is connected the system of hollow cathode, which possesses an entrance of gas and two entrances for its refrigeration, the same is electrically isolated of the rest of the equipment and it is polarized negatively. In front of the system of hollow cathode there is a movable sample in stainless steel with possibility of moving in the horizontal and vertical. In the vertical, the sample can vary its distance between 0 and 70 mm and, in the horizontal, can leave completely from the front of the hollow cathode. The sample and also the cathode hollow are equipped with cromel-alumel termopares with simultaneous reading of the temperatures during the time of treatment. In this work copper electrodes, bronze, titanium, iron, stainless steel, powder of titanium, powder of titanium and silício, glass and ceramic were used. The electrodes were investigated relating their geometry change and behavior of the plasma of the cavity of hollow cathode and channel of the gas. As the cavity of hollow cathode, the analyzed aspects were the diameter and depth. With the channel of the gas, we verified the diameter. In the two situations, we investigated parameters as flow of the gas, pressure, current and applied tension in the electrode, temperature, loss of mass of the electrode with relationship at the time of use. The flow of gas investigated in the electrodes it was fastened in a work strip from 15 to 6 sccm, the constant pressure of work was among 2.7 to 8 x 10-2 mbar. The applied current was among a strip of work from 0,8 to 0,4 A, and their respective tensions were in a strip from 400 to 220 V. Fixing the value of the current, it was possible to lift the curve of the behavior of the tension with the time of use. That curves esteem in that time of use of the electrode to its efficiency is maximum. The temperatures of the electrodes were in the dependence of that curves showing a maximum temperature when the tension was maximum, yet the measured temperatures in the samples showed to be sensitive the variation of the temperature in the electrodes. An accompaniment of the loss of mass of the electrode relating to its time of use showed that the electrodes that appeared the spherical cavities lost more mass in comparison with the electrodes in that didn't appear. That phenomenon is only seen for pressures of 10-2 mbar, in these conditions a plasma column is formed inside of the channel of the gas and in certain points it is concentrated in form of spheres. Those spherical cavities develop inside of the channel of the gas spreading during the whole extension of the channel of the gas. The used electrodes were cut after they could not be more used, however among those electrodes, films that were deposited in alternate times and the electrodes that were used to deposit films in same times, those films were deposited in the glass substrata, alumina, stainless steel 420, stainless steel 316, silício and steel M2. As the eletros used to deposit films in alternate time as the ones that they were used to deposit in same times, the behavior of the thickness of the film obeyed the curve of the tension with relationship the time of use of the electrode, that is, when the tension was maximum, the thickness of the film was also maximum and when the tension was minimum, the thickness was minimum and in the case where the value of the tension was constant, the thickness of the film tends to be constant. The fine films that were produced they had applications with nano stick, bio-compatibility, cellular growth, inhibition of bacterias, cut tool, metallic leagues, brasagem, pineapple fiber and ornamental. In those films it was investigated the thickness, the adherence and the uniformity characterized by sweeping electronic microscopy. Another technique developed to assist the production and characterization of the films produced in that work was the caloteste. It uses a sphere and abrasive to mark the sample with a cap impression, with that cap form it is possible to calculate the thickness of the film. Through the time of life of the cathode, it was possible to evaluate the rate of waste of its material for the different work conditions. Values of waste rate up to 3,2 x 10-6 g/s were verified. For a distance of the substratum of 11 mm, the deposited film was limited to a circular area of 22 mm diameter mm for high pressures and a circular area of 75 mm for pressure strip. The obtained films presented thickness around 2,1 µm, showing that the discharge of arch of hollow cathode in argon obeys a curve characteristic of the tension with the time of life of the eletrodo. The deposition rate obtained in this system it is of approximately 0,18 µm/min
Resumo:
The system built to characterize electrodes and, consequently, deposited fine films are constituted by a hollow cathode that works to discharges and low pressures (approximately 10-3 to 5 mbar), a source DC (0 to 1200 V), a cylindrical camera of closed borossilicato for flanges of stainless steel with an association of vacuum bombs mechanical and spread. In the upper flange it is connected the system of hollow cathode, which possesses an entrance of gas and two entrances for its refrigeration, the same is electrically isolated of the rest of the equipment and it is polarized negatively. In front of the system of hollow cathode there is a movable sample in stainless steel with possibility of moving in the horizontal and vertical. In the vertical, the sample can vary its distance between 0 and 70 mm and, in the horizontal, can leave completely from the front of the hollow cathode. The sample and also the cathode hollow are equipped with cromel-alumel termopares with simultaneous reading of the temperatures during the time of treatment. In this work copper electrodes, bronze, titanium, iron, stainless steel, powder of titanium, powder of titanium and silício, glass and ceramic were used. The electrodes were investigated relating their geometry change and behavior of the plasma of the cavity of hollow cathode and channel of the gas. As the cavity of hollow cathode, the analyzed aspects were the diameter and depth. With the channel of the gas, we verified the diameter. In the two situations, we investigated parameters as flow of the gas, pressure, current and applied tension in the electrode, temperature, loss of mass of the electrode with relationship at the time of use. The flow of gas investigated in the electrodes it was fastened in a work strip from 15 to 6 sccm, the constant pressure of work was among 2.7 to 8 x 10-2 mbar. The applied current was among a strip of work from 0,8 to 0,4 A, and their respective tensions were in a strip from 400 to 220 V. Fixing the value of the current, it was possible to lift the curve of the behavior of the tension with the time of use. That curves esteem in that time of use of the electrode to its efficiency is maximum. The temperatures of the electrodes were in the dependence of that curves showing a maximum temperature when the tension was maximum, yet the measured temperatures in the samples showed to be sensitive the variation of the temperature in the electrodes. An accompaniment of the loss of mass of the electrode relating to its time of use showed that the electrodes that appeared the spherical cavities lost more mass in comparison with the electrodes in that didn't appear. That phenomenon is only seen for pressures of 10-2 mbar, in these conditions a plasma column is formed inside of the channel of the gas and in certain points it is concentrated in form of spheres. Those spherical cavities develop inside of the channel of the gas spreading during the whole extension of the channel of the gas. The used electrodes were cut after they could not be more used, however among those electrodes, films that were deposited in alternate times and the electrodes that were used to deposit films in same times, those films were deposited in the glass substrata, alumina, stainless steel 420, stainless steel 316, silício and steel M2. As the eletros used to deposit films in alternate time as the ones that they were used to deposit in same times, the behavior of the thickness of the film obeyed the curve of the tension with relationship the time of use of the electrode, that is, when the tension was maximum, the thickness of the film was also maximum and when the tension was minimum, the thickness was minimum and in the case where the value of the tension was constant, the thickness of the film tends to be constant. The fine films that were produced they had applications with nano stick, bio-compatibility, cellular growth, inhibition of bacterias, cut tool, metallic leagues, brasagem, pineapple fiber and ornamental. In those films it was investigated the thickness, the adherence and the uniformity characterized by sweeping electronic microscopy. Another technique developed to assist the production and characterization of the films produced in that work was the caloteste. It uses a sphere and abrasive to mark the sample with a cap impression, with that cap form it is possible to calculate the thickness of the film. Through the time of life of the cathode, it was possible to evaluate the rate of waste of its material for the different work conditions. Values of waste rate up to 3,2 x 10-6 g/s were verified. For a distance of the substratum of 11 mm, the deposited film was limited to a circular area of 22 mm diameter mm for high pressures and a circular area of 75 mm for pressure strip. The obtained films presented thickness around 2,1 µm, showing that the discharge of arch of hollow cathode in argon obeys a curve characteristic of the tension with the time of life of the eletrodo. The deposition rate obtained in this system it is of approximately 0,18 µm/min
