scholarly journals A New Version of Spherical Magnetic Curves in the De-Sitter Space S 1 2

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 606 ◽  
Author(s):  
Selçuk Baş
Keyword(s):  
Charged Particle ◽  
Vector Field ◽  
Minkowski Space ◽  
Magnetic Force ◽  
De Sitter Space ◽  
Existence Condition ◽  
De Sitter ◽  
New Type ◽  
Physical Features

This paper presents a new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. In this approach, some geometrical and physical features of the moving charged particle corresponding to the spacelike magnetic curves are identified. An entire characterization is developed for spacelike spherical magnetic curves, denoting particularly the changes of their energy with respect to time, the influence of the magnetic force on them, and the existence condition for the uniformity of these curves.

scholarly journals Constant angle spacelike surface in de Sitter space S₁³

2017 ◽  
Vol 35 (3) ◽  
pp. 79-93
Author(s):  
Tugba Mert ◽  
Baki Karlıga
Keyword(s):  
Vector Field ◽  
De Sitter Space ◽  
Normal Vector ◽  
Spacelike Surface ◽  
De Sitter ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Constant Angle ◽  
Unit Normal Vector Field ◽  
Unit Normal

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

Some remarks on the existence of spacelike hypersurfaces of constant mean curvature

1977 ◽  
Vol 82 (3) ◽  
pp. 489-495 ◽  
Author(s):  
A. J. Goddard
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
General Class ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Minimal Graphs ◽  
Complete Spacelike Hypersurface ◽  
Spacelike Hypersurfaces

AbstractBernstein's theorem states that the only complete minimal graphs in R3 are the hyperplanes. We shall produce evidence in favour of some conjectural generalizations of this theorem for the cases of spacelike hypersurfaces of constant mean curvature in Minkowski space and in de Sitter space. The results suggest that the class of asymptotically simple space-times admitting a complete spacelike hypersurface of constant mean curvature may well be considerably smaller than the general class of asymptotically simple space-times.

scholarly journals NEGATIVE NORM STATES IN DE SITTER SPACE AND QFT WITHOUT RENORMALIZATION PROCEDURE

2002 ◽  
Vol 11 (06) ◽  
pp. 509-518 ◽  
Author(s):  
MOHAMMAD VAHID TAKOOK
Keyword(s):  
Minkowski Space ◽  
De Sitter Space ◽  
Infrared Divergence ◽  
Space Time ◽  
Ultraviolet Divergence ◽  
De Sitter ◽  
Physical Content ◽  
Negative Norm ◽  
Minkowski Space Time ◽  
Loop Approximation

In recent papers,1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy2 and infrared divergence in the two point function.3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation.

Nonsingular Metric Elastic Universe

1996 ◽  
Vol 168 ◽  
pp. 571-572
Author(s):  
Alexander Gusev
Keyword(s):  
Phase Space ◽  
Minkowski Space ◽  
Vacuum State ◽  
De Sitter Space ◽  
Space Time ◽  
Phase Portraits ◽  
De Sitter ◽  
Deformation State ◽  
Image Position ◽  
The Universe

In the RTFD(Gusev (1986)) the conception of a Sakharov - Wheeler Metric Elasticity(SWME)(Sakharov (1967), Wheeler (1970)) had been worked out. On the basis of the exact solutions of Einstein equations and qualitative analysis RTFD the global evolution have been studied and the phase portraits of the early Universe is being constructed. An analysis of phase portraits show on the possibility description of spontaneous creation of Universe from an initial Minkowskian's vacuum to an inflationary de Sitter space-time in the frame of phenomenological non-quantum theory (Guth (1991)). During the past decade, a radically new picture of cosmology has emerged. The present homogeneous expanding Universe would have stated out with a de Sitter phase. The purpose of this paper is to shown that the geometry-dynamical approach to the Einstein's gravitation theory in the frame RTFD also is leaded to the nonsingular cosmological models (Brandenberger (1993)). Let us to propose that before the some moment of time the Universe is at the vacuum state and is described the geometry of Minkowskian's space. Deformations of vacuum state, identifying with empty Mikowskian's space are described by the deformations tensor, An arising of deformation ∊αβis leaded to appearance of the stress tensor ∊αβand the energy-momentumTαβ(∊γδ) which is connected with “creating” particles in the Universe. Here we are considered the deformations of Minkowskian's space (the initial vacuum state with∞αβ = 0) at the linear theory (~ ∊) of finite deformations. The final deformation stategαβare searched in the metric class of Friedmann's cosmological spaces. In the comoving reference systemUα(0, 0, 0, 1) the Friedmann's equations have form (Narlikar & Padmanabhan (1983), and Gusev (1989)):where R(t) is so called the expansion factor at the Robertson - Walker line element, k is the curvature parameter with the possible values −1, 0, + 1, P is pressure,k1,k2are the some combination from a Lame coefficients,l02is a “initial radius” Universe, a free parameter model. The phase space of this model is the two-dimensional (R,Ṙ) plane. We note that there is only two singular points (Ṙ= 0,Ṙ= 0) in the phase plane. The one of those points isR=l0,Ṙ= 0 and corresponds to Minkowski space - time. There are two classes trajectories which are asymptotically de Sitter. Those starting at large positive values ofṘgo off toṘ= + ∞, reaching their asymptotic value of H from above. Those starting with large negative values ofṘtend toR= + ∞ withṘ> 0. For small values ofṘand R we can see that there are periodic solutions about Minkowski space. The corresponding solutions oscillate with frequency given byH0(which is possible equal planck scale) about Minkowski space. Based on the preceding discussion of asymptotic solutions we see that there is a separatrix (Gusev, (1989)) in phase space dividing solutions which tend toR= + ∞ from those which oscillate or tend toR=l0. The above analyses of the phase portraits is an indication that in our theory Minkowski space may be unstable toward homogeneous deformations. We stress that all the general features of the phase portrait analyses are true for quadratic deformations of gravitational vacuum. Our model incorporates a very important feature: in the asymptotic de Sitter region, the quadratic deformations and temperature effects does not have an important effect on the geometry. The effective gravitational constant of coupling goes to zero as space - time approaches de Sitter space. In this sense the model is asymptotically free (gravitational confinement Linde, (1990)). At the late times the solutions are described a evolution of the de Sitter UniverseR~expHt(Hoyle et al. (1993)).

HOW HOT IS THE DE SITTER SPACE?

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1507-1520 ◽  
Author(s):  
H. NARNHOFER ◽  
I. PETER ◽  
W. THIRRING
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
De Sitter Space ◽  
Killing Vector Field ◽  
Quantum Fields ◽  
De Sitter

We show that the unique invariant locally Minkowskian state of quantum fields in de Sitter space M has for an observer moving along with a Killing vector field a temperature [Formula: see text] where R is the radius of M and a his acceleration. States with another temperature cannot be locally Minkowskian all over M.

scholarly journals Optical electromagnetic radiation density spherical geometric electric and magnetic phase by spherical antiferromagnetic model with fractional system

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
E. M. Khalil ◽  
T. K¨orpinar ◽  
Z. K¨orpinar ◽  
Mustafa Inc
Keyword(s):  
Electromagnetic Radiation ◽  
Numerical Solutions ◽  
De Sitter Space ◽  
De Sitter ◽  
Radiation Density ◽  
Fractional Equations ◽  
Magnetic Flows ◽  
Electromagnetic Fluid ◽  
New Type ◽  
Antiferromagnetic Model

In this article, we firstly consider a new theory of spherical electromagnetic radiation density with antiferromagnetic spin of timelike spherical t -magnetic flows by the spherical Sitter frame in de Sitter space. Thus, we construct the new relationship between the new type electric and magnetic phases and spherical timelike magnetic flows de Sitter space 2.1 S Also, we give the applied geometric characterization for spherical electromagnetic radiation density. This concept also boosts to discover some physical and geometrical characterizations belonging to the particle. Moreover, the solution of the fractional-order systems are considered for the submitted mathematical designs. Graphical demonstrations for fractional solutions are presented to expression of the approach. The collected results illustrate that mechanism is relevant and decisive approach to recover numerical solutions of our new fractional equations. Components of performed equations are demonstrated by using approximately explicit values of physical assertions on received solutions. Finally, we constructthat electromagnetic fluid propagation along fractional optical fiber indicates an fascinating family of fractional evolution equation with diverse physical and applied geometric modelling in de Sitter space 2 1 S .

scholarly journals ON THE UNRUH EFFECT IN DE SITTER SPACE

2011 ◽  
Vol 26 (28) ◽  
pp. 2149-2158 ◽  
Author(s):  
R. CASADIO ◽  
S. CHIODINI ◽  
A. ORLANDI ◽  
G. ACQUAVIVA ◽  
R. DI CRISCIENZO ◽  
...  
Keyword(s):  
Vector Field ◽  
Proper Motion ◽  
Quantum Noise ◽  
De Sitter Space ◽  
Unruh Effect ◽  
Back Reaction ◽  
De Sitter ◽  
Sitter Universe ◽  
De Sitter Universe

We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static spacetimes, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector field are stable.

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