Gravitational Perturbation of Traversable Wormhole Spacetime and the Stability

2018 ◽  
Vol 73 (12) ◽  
pp. 1800-1807 ◽  
Author(s):  
YuRi Kang ◽  
Sung-Won Kim
Keyword(s):  
Gravitational Perturbation ◽  
Traversable Wormhole ◽  
The Stability

scholarly journals On the existence and stability of traversable wormhole solutions in modified theories of gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Oleksii Sokoliuk ◽  
Alexander Baransky
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Traversable Wormhole ◽  
Existence And Stability ◽  
Theories Of Gravity ◽  
The Stability

AbstractWe study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$ f ( R ) = R + a R 2 , power-law $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$ f ( R ) = f 0 R n , log-corrected $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$ f ( R ) = R + α R 2 + β R 2 ln β R theories, and finally on the exponential hybrid metric-Palatini gravity $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$ f ( R ^ ) = ζ ( 1 + e - R ^ Φ ) . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state $$p_t=\omega \rho $$ p t = ω ρ . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

Reconstruction of f(T) gravity in the context of standard Chaplygin gas as tachyon scalar field and study of the stability against gravitational perturbation

2019 ◽  
Vol 16 (07) ◽  
pp. 1950101
Author(s):  
Surajit Chattopadhyay ◽  
Soumyodipta Karmakar
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
State Parameter ◽  
Chaplygin Gas ◽  
Gravitational Perturbation ◽  
Gravitational Perturbations ◽  
Equation Of State Parameter ◽  
Speed Parameter ◽  
The Stability ◽  
The Universe

The present paper reports a study on the [Formula: see text] gravity reconstruction scheme in the context of considering standard Chaplygin gas as tachyon scalar field model of dark energy. The solution for reconstructed [Formula: see text] gravity has been obtained from reconstructed potential and scalar field of tachyon based on the standard Chaplygin gas. It has been observed that the equation of state parameter due to the reconstructed torsion contribution to the density and pressure behaves like quintom and is consistent with the observational value of the equation of state parameter for the current universe. The reconstructed [Formula: see text] has then been tested for gravitational perturbation by deriving the frictional term, the effective mass and the sound speed parameter for the gravitational potential and it has been found to be stable against gravitational perturbations through positive value of the squared speed of sound. Finally, statefinder diagnostics has been carried out and the reconstructed [Formula: see text] gravity is found to interpolate between dust and [Formula: see text]CDM phases of the universe.

Traversable wormhole modelling with exponential and hyperbolic shape functions in F(R,T) framework

2020 ◽  
Vol 35 (25) ◽  
pp. 2050149
Author(s):  
Shweta ◽  
Ambuj Kumar Mishra ◽  
Umesh Kumar Sharma
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Gravitational Theory ◽  
Null Energy Condition ◽  
Relativity Theory ◽  
Shape Functions ◽  
Traversable Wormhole ◽  
Hydrostatic Force ◽  
State Formula ◽  
The Stability

The concept of traversable wormhole, a hypothetical tunnel-like structure is initially proposed by Morris and Thorne (Am. J. Phys. 56, 395 (1988)) by using Einstein’s general relativity theory. Harko et al. (Phys. Rev. D 84, 024020 (2011)) defined [Formula: see text] gravity as an extended gravitational theory having terms [Formula: see text] and [Formula: see text] as Ricci scalar and trace of energy momentum respectively. In this article, we explore wormhole models for the framework of [Formula: see text] gravity by using two different shape functions. The first shape function is [Formula: see text], [Formula: see text] (proposed by Mishra and Sharma, arXiv:2003.00298v1 , 2020) and second is a hyperbolic shape function which is of the form [Formula: see text]. Geometrical behavior of wormholes are discussed in anisotropic scenario by using equation of state [Formula: see text]. The stability of models are analyzed by using equilibrium condition and determining gravitational force, anisotropic force, hydrostatic force and force due to modified gravity. For the validation of null energy condition and weak energy condition, significant role of shape function is illustrated for the presence of nonexotic matter.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

1970 ◽  
Vol 28 ◽  
pp. 444-445
Author(s):  
E. R. Kimmel ◽  
H. L. Anthony ◽  
W. Scheithauer
Keyword(s):  
High Temperature ◽  
Metal Matrix ◽  
Oxide Particle ◽  
Oxide Phase ◽  
Dislocation Motion ◽  
Particle Dispersion ◽  
High Temperature Strength ◽  
Strengthening Effect ◽  
Oxide Particles ◽  
The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Formation and Structure of Casein Micelles in Lactating Mammary Tissue

1970 ◽  
Vol 28 ◽  
pp. 150-151
Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell
Keyword(s):  
Size Distribution ◽  
G Protein ◽  
Milk Proteins ◽  
Mammary Tissue ◽  
Colloidal System ◽  
Casein Micelles ◽  
The Stability

Milk is an unusually stable colloidal system; the stability of this system is due primarily to the formation of micelles by the major milk proteins, the caseins. Numerous models for the structure of casein micelles have been proposed; these models have been formulated on the basis of in vitro studies. Synthetic casein micelles (i.e., those formed by mixing the purified αsl- and k-caseins with Ca2+ in appropriate ratios) are dissimilar to those from freshly-drawn milks in (i) size distribution, (ii) ratio of Ca/P, and (iii) solvation (g. water/g. protein). Evidently, in vivo organization of the caseins into the micellar form occurs in-a manner which is not identical to the in vitro mode of formation.

TEM Analysis of Long-Period Polytypes in SiC—S

1976 ◽  
Vol 34 ◽  
pp. 630-631
Author(s):  
S. Shinozaki ◽  
J. W. Sprys
Keyword(s):  
Electron Diffraction ◽  
Isothermal Annealing ◽  
Tem Analysis ◽  
Long Period ◽  
Transmission Electron ◽  
Average Grain Size ◽  
High Resolution Tem ◽  
Structural Lattice ◽  
The Stability ◽  
Continuous Curves

In reaction sintered SiC (∽ 5um average grain size), about 15% of the grains were found to have long-period structures, which were identifiable by transmission electron microscopy (TEM). In order to investigate the stability of the long-period polytypes at high temperature, crystal structures as well as microstructural changes in the long-period polytypes were analyzed as a function of time in isothermal annealing.Each polytype was analyzed by two methods: (1) Electron diffraction, and (2) Electron micrograph analysis. Fig. 1 shows microdensitometer traces of ED patterns (continuous curves) and calculated intensities (vertical lines) along 10.l row for 6H and 84R (Ramsdell notation). Intensity distributions were calculated based on the Zhdanov notation of (33) for 6H and [ (33)3 (32)2 ]3 for 84R. Because of the dynamical effect in electron diffraction, the observed intensities do not exactly coincide with those intensities obtained by structure factor calculations. Fig. 2 shows the high resolution TEM micrographs, where the striped patterns correspond to direct resolution of the structural lattice periodicities of 6H and 84R structures and the spacings shown in the figures are as expected for those structures.

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