scholarly journals Magnetized Dusty Black Holes and Wormholes

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 419
Author(s):  
Kirill A. Bronnikov ◽  
Pavel E. Kashargin ◽  
Sergey V. Sushkov
Keyword(s):  
Numerical Study ◽  
Dust Cloud ◽  
Fixed Time ◽  
Time Instant ◽  
Space Time ◽  
Radial Coordinate ◽  
Timelike Vector ◽  
Maximum Expansion ◽  
Dust Clouds ◽  
Finite Period

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions f(R), F(R) and τ0(R), where R is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (f>0), parabolic (f=0) and elliptic (f<0) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.

scholarly journals Determination of the order of fractional derivative for subdiffusion equations

2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov
Keyword(s):  
Fractional Derivative ◽  
Fixed Time ◽  
Time Instant ◽  
Observation Data ◽  
Additional Information ◽  
Fractional Modeling ◽  
Time Fractional Derivative ◽  
The Right ◽  
Right Order

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.

Looking Forward Approach in Cooperative Differential Games

2016 ◽  
Vol 18 (02) ◽  
pp. 1640007 ◽  
Author(s):  
Petrosian Ovanes
Keyword(s):  
Differential Games ◽  
Fixed Time ◽  
Time Instant ◽  
Time Interval ◽  
New Approach ◽  
Game Dynamics ◽  
Motion Equations ◽  
Payoff Functions ◽  
Definition Of ◽  
Cooperative Differential Games

New approach to the definition of solution in cooperative differential games is considered. The approach is based on artificially truncated information about the game. It assumed that at each time, instant players have information about the structure of the game (payoff functions, motion equations) only for the next fixed time interval. Based on this information they make the decision. Looking Forward Approach is applied to the cases when the players are not sure about the dynamics of the game on the whole time interval [Formula: see text] and orient themselves on the game dynamics defined on the smaller time interval [Formula: see text] ([Formula: see text]), on which they surely know that the game dynamics is not changing.

Non-Linear Space-Time Evolution of Wave Groups With a High Crest

2003 ◽  
Author(s):  
Felice Arena ◽  
Francesco Fedele
Keyword(s):  
Time Evolution ◽  
Field Experiments ◽  
Surface Displacement ◽  
Fixed Time ◽  
Space Time ◽  
Second Order ◽  
Small Scale ◽  
Free Surface Displacement ◽  
Non Linear ◽  
Space Time Evolution

The theory of quasi-determinism, for the mechanics of linear three-dimensional waves, was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. The theory was verified in the nineties with some small-scale field experiments. In this paper the first formulation of Boccotti’s theory, valid for the space-time domain, is extended to the second order. The analytical expressions of the non-linear free surface displacement and velocity potential are obtained. Therefore the space-time evolution of a wave group, to the second-order in a Stokes expansion, when a very large crest occurs at a fixed time and location, is investigated. Finally the second-order probability of exceedance of the crest amplitude is obtained, as a function of two deterministic parameters.

INHOMOGENEOUS DUST COLLAPSE WITH COSMOLOGICAL CONSTANT

2005 ◽  
Vol 14 (03n04) ◽  
pp. 707-715 ◽  
Author(s):  
S. G. GHOSH
Keyword(s):  
Cosmological Constant ◽  
Gravitational Collapse ◽  
Dust Cloud ◽  
Cosmic Censorship ◽  
Space Time ◽  
De Sitter ◽  
Naked Singularities ◽  
Asymptotic Flatness ◽  
Sitter Background ◽  
Strong Curvature

We investigate the occurrence of naked singularities in the gravitational collapse of an inhomogeneous dust cloud in an expanding de Sitter background — a piece of Tolman–Bondi–de Sitter space–time. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. Our result unambiguously support the fact that the asymptotic flatness of space–time is not a necessary ingredient for the development of naked singularities.

scholarly journals GALILEAN CONFORMAL ALGEBRA IN SEMI-INFINITE SPACE

2012 ◽  
Vol 27 (09) ◽  
pp. 1250044
Author(s):  
M. R. SETARE ◽  
V. KAMALI
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Correlation Functions ◽  
Fixed Time ◽  
Space Time ◽  
Conformal Algebra ◽  
Infinite Space ◽  
Conformal Algebras

In the present paper, we considered Galilean conformal algebras (GCAs), which arises as a contraction relativistic conformal algebras (xi→ϵxi, t→t, ϵ→0). We can use the Galilean conformal (GC) symmetry to constrain two-point and three-point functions. Correlation functions in space–time without boundary condition were found [A. Bagchi and I. Mandal, Phys. Lett. B675, 393 (2009).]. In real situations, there are boundary conditions in space–time, so we have calculated correlation functions for GC invariant fields in semi-infinite space with boundary condition in r = 0. We have calculated two-point and three-point functions with boundary condition in fixed time.

Flow visualisation of the helicopter brown-out phenomenon

2009 ◽  
Vol 113 (1145) ◽  
pp. 467-478 ◽  
Author(s):  
N. D. Nathan ◽  
R. B. Green
Keyword(s):  
Particle Image ◽  
Dust Cloud ◽  
Ground Effect ◽  
Flow Visualisation ◽  
Forward Speed ◽  
Fine Dust ◽  
Dust Clouds ◽  
Image Velocimetry ◽  
Series Of Experiments ◽  
The Mean

Abstract Quantitative and qualitative results of a series of experiments conducted on a rotor in ground effect at low forward speeds are presented. The velocity over a wide area of the ground effect wake was measured using particle image velocimetry, and the evolution of the flow is described as the forward speed increases. The formation of a dust cloud leading to so-called helicopter brown-out was simulated through a series of flow visualisation experiments. The technique involved sprinkling a fine dust on the ground below and ahead of the rotor. Larger dust clouds were observed at lower forward speed, and the dust cloud penetrated into the areas of the flow including those where vorticity levels were of low magnitude and occasional velocity fluctuations from the mean were large.

Nonlinear Space–Time Evolution of Wave Groups With a High Crest

2005 ◽  
Vol 127 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Felice Arena ◽  
Francesco Fedele
Keyword(s):  
Time Evolution ◽  
Surface Displacement ◽  
Fixed Time ◽  
Space Time ◽  
Second Order ◽  
Random Wave ◽  
Wave Groups ◽  
Free Surface Displacement ◽  
Nonlinear Free Surface ◽  
Space Time Evolution

The theory of quasi-determinism, for the mechanics of linear random wave groups was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. In this paper the first formulation of Boccotti’s theory, particularized for long-crested waves, is extended to the second-order. The analytical expressions of the nonlinear free surface displacement and velocity potential are obtained. The space–time evolution of the nonlinear wave group, when a very large crest occurs at a fixed time and location, is then shown. Finally the second-order probability of exceedance of the crest amplitude is obtained and validated by Monte Carlo simulation.

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